According to the online critique of Explore Evolution by the National Center for Science Education (NCSE):
(A) EE falsely claims that Darwin accepted Ernst Haeckel's Biogenetic Law that "ontogeny recapitulates phylogeny." In particular, the claim in EE that "Darwin thought that the observable similarities in different embryos revealed what the ancestors to these organisms would have looked like" [p. 66 of EE] "contradicts the majority view of prominent Darwin scholars (including Ernst Mayr, Stephen Jay Gould, David Hull, and Peter Bowler)." 
(B) EE "falsely asserts Darwin thought the similarities between embryos were greater at the earliest stages of development," and falsely suggests "that common descent and Haeckel's Biogenetic Law require that the earliest stages of animal development are most similar." But Darwin actually thought that "embryos at the earliest stages of development can vary significantly from one another depending upon the amount of yolk in their eggs." 
(C) EE's claim that Haeckel's misrepresentation of vertebrate embryos "remains in many modern high school and college biology textbooks" is false, as shown by "a recent survey of 36 biology textbooks." 
(A) Darwin and Haeckel's Biogenetic Law
Haeckel's Biogenetic Law claims that the stages through which embryos pass during their development ("ontogeny") replay ("recapitulate") the evolutionary history of the species ("phylogeny"). Haeckel believed that this was due to the addition of new features to the adult in the course of evolution, causing more primitive features to be pushed deeper into embryo development. According to B. I. Balinsky's classic textbook, Introduction to Embryology (1975), the Biogenetic Law states that "features of ancient origin develop early in ontogeny; features of newer origin develop late. Hence, the ontogenetic development presents the various features of the animal's organization in the same sequence as they evolved during the phylogenetic development. Ontogeny is a recapitulation of phylogeny." 
As a claim that embryos recapitulate the adult forms of their ancestors, Haeckel's Biogenetic Law was discredited in the early decades of the twentieth century. American embryologist Frank Lillie wrote that "it never happens that the embryo of any definite species resembles in its entirety the adult of a lower species." British embryologist Walter Garstang criticized Haeckel's biogenetic law as "demonstrably unsound," because "ontogenetic stages afford not the slightest evidence of the specially adult features of the ancestry." According to Garstang, Haeckel's theory that newly evolved features are simply tacked onto the end of development makes no sense: "A house is not a cottage with an extra story on the top. A house represents a higher grade in the evolution of a residence, but the whole building is altered--foundations, timbers, and roof--even if the bricks are the same." 
So embryos do not recapitulate the adult forms of their ancestors. Modern apologists for Darwinism sometimes claim that they recapitulate the embryos of their ancestors, but fossil embryos are extremely rare, so this claim is not supported by the fossil record. Instead, it is typically defended by referring to embryos of modern organisms that are assumed to resemble ancestral organisms. In other words, the comparisons are based on the assumption that Darwin's theory is true--though the truth or falsity of the theory is the very question the comparisons are supposed to answer.
In any case, the NCSE critique is mistaken: Darwin actually embraced Haeckel's original idea that modern embryos resemble the adults of their ancestors. The NCSE critique appeals to the authority of some "prominent Darwin scholars," but Darwin's actual words contradict those scholars:
"With some animals the successive variations may have supervened at a very early period of life, or the steps may have been inherited at an earlier age than that at which they first occurred. In either of these cases, the young or embryo will closely resemble the mature parent-form." (The Origin of Species, 6th edition, p. 393)
"It is highly probable that with many animals the embryonic or larval stages show us, more or less completely, the condition of the progenitor of the whole group in its adult state." (op. cit., p. 395)
"As the embryo often shows us more or less plainly the structure of the less modified and ancient progenitor of the group, we can see why ancient and extinct forms so often resemble in their adult state the embryos of existing species of the same class." (op. cit., p. 396)
"Embryology rises greatly in interest, when we look at the embryo as a picture, more or less obscured, of the progenitor, either in its adult or larval state, of all the members of the same great class." (op. cit., p. 396) 
(B) Darwin and the Earliest Stages of Embryological Development
In The Origin of Species, Darwin explicitly cited Karl Ernst von Baer's view that embryos are most alike in their earliest stages: "The embryos of mammalia, of birds, lizards, and snakes, probably also of chelonia [turtles], are in their earliest states exceedingly like one another, both as a whole and in the mode of development of their parts; so much so, in fact, that we can often distinguish the embryos only by their size."
Embryologist Adam Sedgwick pointed out in 1894 that von Baer's view doesn't fit the evidence. The NCSE Critique claims that Sedgwick's criticism has no bearing on Darwin's view--but this is false, since Darwin explicitly relied on von Baer. The NCSE Critique also devotes several pages to discrediting Sedgwick, but modern biologists have confirmed his criticism of von Baer. For example, Dartmouth embryologist William Ballard wrote in 1976 that it is "only by semantic tricks and subjective selection of evidence," by "bending the facts of nature," that one can argue that the early stages of vertebrates "are more alike than their adults." Indiana University biologist Rudolf Raff wrote in 1996: "It should be noted that von Baer's laws provide an incomplete description of development," since despite his statement about the earliest stages he was "was dealing only with the latter half of ontogeny." 
Darwin acknowledged exceptions to his view that embryos are most similar in their early stages. A larva could adapt "to its conditions of life," and "owing to such adaptations, the similarity of the larvae of allied animals is sometimes greatly obscured." According to the NCSE Critique, Darwin also thought that "embryos at the earliest stages of development can vary significantly from one another depending upon the amount of yolk in their eggs." But Darwin did not mention variations due to the amount of yolk; this idea was proposed much later.  Although the NCSE Critique's attack on EE's treatment of embryology is largely historical, its "history" is flawed.
In any case, Darwin regarded larval differences as exceptions to the general rule that "the embryos of the most distinct species belonging to the same class are closely similar, but become, when fully developed, widely dissimilar." Thus "community in embryonic structure reveals community of descent; but dissimilarity in embryonic development does not prove discommunity of descent, for in one of two groups the developmental stages may have been suppressed, or may have been so greatly modified through adaptation to new habits of life, as to be no longer recognizable." 
Although some larvae are exceptions, Darwin thought that as a general rule the embryos of the same group are most similar in their earliest stages, and that differences appear later in development. This pattern is a logical consequence of Darwin's theory that new features arising in the course of evolution are added at the end of development. Thus the NCSE's claim that Darwin did not insist on similarity in the earliest stages of development is refuted not only by the sentence quoted above from von Baer, but also by Darwin's own logic.
Unfortunately for Darwin, larvae are not the only exception to the pattern of early similarity followed by later dissimilarity. Vertebrate embryos, for example, start out very different from each other. They converge somewhat in appearance midway through development, at the stage Haeckel represented as the first in his infamous drawings, then they diverge again as they develop to adulthood. This pattern is well known; Swiss biologist Denis Duboule calls it a "development egg-timer," while American biologist Rudolf Raff calls it a "developmental hourglass."  So contrary to Darwin's thinking, the general pattern is not early similarity followed by later dissimilarity, but early dissimilarity followed by similarity and then again by dissimilarity.
(C) Haeckel and Recent Biology Textbooks
The NCSE critique's claim that recent biology textbooks do not include Haeckel's misrepresentation of vertebrate embryos is false. In 2000, Stephen Jay Gould lamented the fact that biology textbooks were continuing to rely on Haeckel's drawings--which Gould called "exaggerated" and even "fraudulent." "We do, I think, have the right," he wrote, "to be both astonished and ashamed by the century of mindless recycling that has led to the persistence of these drawings in a large number, if not a majority, of modern textbooks." 
In response to Gould's essay (and to Jonathan Wells's Icons of Evolution, published the same year), some textbook-writers began removing the embryo drawings from new editions of their books. For example, Haeckel's drawings had appeared in the third edition of Molecular Biology of the Cell (1994), but lead author Bruce Alberts told The New York Times in 2001 that they would be removed from the fourth edition. 
Yet fully half of the 36 textbooks cited by the NCSE Critique were published after 2000--the year the drawings finally began to disappear. And the list omits the following textbooks published between 1998 and 2004 that do include Haeckel's drawings or a re-drawn version of them:
â€¢ Biggs, Kapicka & Lundgren, Biology: The Dynamics of Life (Glencoe, 1998)
â€¢ Johnson, Biology: Visualizing Life (Holt, Rinehart & Winston, 1998)
â€¢ Douglas J. Futuyma, Evolutionary Biology (Sinauer, 1998)
â€¢ Miller & Levine, Biology, 4th Edition (Prentice Hall, 1998)
â€¢ Miller & Levine, Biology: The Living Science (Prentice Hall, 1998)
â€¢ Raven & Johnson, Biology, 5th Edition (McGraw-Hill, 1999)
â€¢ Schraer & Stoltze, Biology: The Study of Life, 7th Edition (1999)
â€¢ Miller & Levine, Biology, 5th Edition (Prentice Hall, 2000)
â€¢ Padilla, Focus on Life Science, California Edition (Prentice Hall, 2001)
â€¢ Raven & Johnson, Biology, 6th Edition (McGraw-Hill, 2002)
â€¢ Donald & Judith Voet, Biochemistry, 3rd Edition (Wiley, 2004)
Not only does the NCSE's list selectively omit many textbooks, but it also misrepresents the textbooks it includes. For example, the list cites the following textbooks and claims that they do not contain Haeckel's drawings; yet all three contain either Haeckel's drawings or a redrawn version of them:
â€¢ Alberts, Bray, Lewis, Raff, Roberts & Watson, Molecular Biology of the Cell (Garland, 1994)
â€¢ Starr & Taggart, Biology: The Unity and Diversity of Life, 8th Edition (Wadsworth, 1998)
â€¢ Guttman, Biology (McGraw-Hill, 1999)
The NCSE's false claims about the contents of recent biology textbooks are similar to those made by Darwinist Randy Olson in his 2006 film Flock of Dodos.  Like Olson, the NCSE is clearly more committed to protecting Darwinism from critical challenges than to acknowledging the truth.
 National Center for Science Education (NCSE). Sept. 30, 2008. Critique of Explore Evolution. Section on "Ontogeny and Phylogeny," http://ncseweb.org/creationism/analysis/ontongeny-phylogeny.
 Ibid. "Haeckel's Drawings," http://ncseweb.org/creationism/analysis/haeckels-drawings; "Exaggerations," http://ncseweb.org/creationism/analysis/exaggerations; "The Earliest Stages," http://ncseweb.org/creationism/analysis/earliest-stages; "Sedgwick's Two Challenges," http://ncseweb.org/creationism/analysis/sedgwicks-two-challenges.
 Ibid. "Richardson," http://ncseweb.org/creationism/analysis/richardson.
 B. I. Balinsky, An Introduction to Embryology, Fourth Edition. Philadelphia: W. B. Saunders Company, 1975, pp. 7-8; Stephen Jay Gould, Ontogeny and Phylogeny. Cambridge, MA: Harvard University Press, 1977, p. 168.
 Frank R. Lillie, The Development of the Chick, Second Edition. New York: Henry Holt, 1919, pp. 4-6; Walter Garstang, "The theory of recapitulation: a critical restatement of the biogenetic law," Journal of the Linnean Society (Zoology), 35 (1922): 81-101; Gavin de Beer, Embryos and Ancestors, Third Edition. Oxford: Clarendon Press, 1958, pp. 10, 164, 172; Nicolas Rasmussen, "The Decline of Recapitulationism in Early Twentieth-Century Biology: Disciplinary Conflict and Consensus on the Battleground of Theory," Journal of the History of Biology 24 (1991): 51-89; Scott F. Gilbert, "Ernst Haeckel and the Biogenetic Law," from Chapter 23 of Developmental Biology, Eighth Edition. Sunderland, MA: Sinauer Associates, 2006. Available online (2008) at http://8e.devbio.com/article.php?id=219.
 Charles Darwin, The Origin of Species, Sixth Edition. London: John Murray, 1872. Available online (2008) at http://darwin-online.org.uk/content/frameset?viewtype=side&itemID=F391&pageseq=415. See also Robert Richards, The Meaning of Evolution. Chicago" The University of Chicago Press, 1992, pp. 169-174.
 Darwin, The Origin of Species, Sixth Edition, pp. 387-388. Available online (2008) at http://darwin-online.org.uk/content/frameset?viewtype=side&itemID=F391&pageseq=415.
 Adam Sedgwick, "On the Law of Development commonly known as von Baer's Law; and on the Significance of Ancestral Rudiments in Embryonic Development," Quarterly Journal of Microscopical Science 36 (1894): 35-52; NCSE, critique (September 30, 2008). NCSE, Critique of Explore Evolution. "Sedgwick's Two Challenges." Available online (2008) at http://ncseweb.org/creationism/analysis/sedgwicks-two-challenges; William W. Ballard, "Problems of gastrulation: real and verbal," BioScience 26 (1976): 36-39; Rudolf A. Raff, The Shape of Life: Genes, Development, and the Evolution of Animal Form. Chicago: The University of Chicago Press, 1996, p. 197; Jonathan Wells, "Haeckel's Embryos and Evolution: Setting the Record Straight," The American Biology Teacher 61 (May, 1999): 345-349. Available online (2008) at http://www.discovery.org/a/3071.
 Darwin, The Origin of Species, Sixth Edition, p. 389. Available online (2008) at http://darwin-online.org.uk/content/frameset?viewtype=side&itemID=F391&pageseq=415. For example, see Richard P. Elinson, "Change in developmental patterns: embryos of amphibians with large eggs," pp. 1-21 in R. A. Raff & E. C. Raff (editors), Development as an Evolutionary Process, Volume 8. New York: Alan R. Liss, 1987, p. 3.
 Darwin, The Origin of Species, Sixth Edition, pp. 387, 396. Available online (2008) at http://darwin-online.org.uk/content/frameset?viewtype=side&itemID=F391&pageseq=415.
 Denis Duboule, "Temporal colinearity and the phylotypic progression: a basis for the stability of a vertebrate Bauplan and the evolution of morphologies through heterochrony," Development Supplement (1994): 135-142; Raff, The Shape of Life, p. 197; Jonathan Wells, Icons of Evolution: Why Much of What We Teach About Evolution Is Wrong. Washington, DC: Regnery Publishing, 2000, Chapter 5. More information available online (2008) at http://www.iconsofevolution.com/.
 Stephen Jay Gould, "Abscheulich! Atrocious!" Natural History (March, 2000): 42-49.
 James Glanz, "Biology Text Illustrations More Fiction Than Fact," The New York Times (April 8, 2001). Available online (2008) at http://query.nytimes.com/gst/fullpage.html?res=990DE3DB103EF93BA35757C0A9679C8B63.
 John G. West & Casey Luskin, "Hoax of Dodos, pt. 1: Flock of Dodos Filmmaker Wrongly Claims Haeckel's Embryo Drawings Weren't in Modern Textbooks," Discovery Institute (February 7, 2007). Available online (2008) at
http://www.evolutionnews.org/2007/02/hoax_of_dodos_pt_1_flock_of_do.html; Jonathan Wells, "Flock of Dodos, or Pack of Lies?" Discovery Institute (February 9, 2007). Available online (2008) at http://www.evolutionnews.org/2007/02/flock_of_dodos_or_pack_of_fals_4.html; Jonathan Wells, "The Cracked Haeckel Approach to Evolutionary Reasoning," Evolution News & Views (February 17, 2007). Available online (2008) at http://www.evolutionnews.org/2007/02/the_cracked_haeckel_approach_t.html; Casey Luskin, "What do Modern Textbooks Really Say about Haeckel's Embryos?" Discovery Institute (March 27, 2007). Available online (2008) at
http://www.discovery.org/scripts/viewDB/index.php?command=view&id=3935&program=CSC%20-%20Scientific%20Research%20and%20Scholarship%20-%20Science; Discovery Institute Staff, "Olson's Hoax on Haeckel's Embryos: Flock of Dodos Filmmaker Claims Haeckel's Embryo Drawings Weren't in Modern Textbooks--But They Really Are." Discovery Institute (May 11, 2007). Available online (2008) at