Algicides. Forget the poisons. There are some ineffective and dangerous ways to "nuke" algae with poisons, but you should ignore them. Water additives formulated for pond use and touted to kill algae generally contain simazine or copper, or both, drugs that are too toxic to fish and plants and too difficult to control for them to be recommendable within the confines of an aquarium.
Simazine. Too fine a line distinguishes a dosage of simazine that will kill algae from one that will shock the higher plants into a slow irreversible decline. Distributors have changed their tone from "may affect plant growth" to limiting recommended use to fountains, ponds and aquaria "containing no live plants." The shock to plants simazine causes won't show in the first days, by the way. Since a simazine-based algae-control product still being marketed to pondkeepers is touted as containing "EPA-registered" ingredients, it's worth following up at the official Environmental Protection Agency website. where you can also do a search for "simazine" in order to see how the E.P.A. actually does "register" simazine. I discovered at the site that it's a pre-emergent herbicide that doesn't bind to sediments nor evaporate; in fact it's persistent for "a few months to a few years," rather a long time in an aquarium. In 1992 Ciba-Geigy voluntarily withdrew the registration of simazine from all aquatic uses: aquariums, ponds, fish hatchery ponds, ornamental ponds, ornamental fountains, and swimming pools, and informed formulators that support for these uses was being withdrawn. Products like Proguard Algae-gone have disappeared from commerce.
Simazine, banned since 1991 in the European Union, is one of the herbicides called triazines that have been under an EPA "special review" since 1994. DuPont (apparently sensing the direction the wind was blowing) agreed to phase out its proprietary triazine, called cyanazine and marketed as Bladex, by the end of 1999, though they didn't want to connect their action with studies implicating the chemical in cancer or studies finding that it was showing up in drinking water supplies in heavy agribusiness areas like the Midwest. Other agribusiness lobbying have kept simazine and other triazines on the market, for now.
Back in 1986, before these reservations surfaced, Neil Frank published an article on the action of simazine, the gist of which is archived at TheKrib. If you're considering using simazine to control algae, read Neil Frank's article.
Polyquat. A less-destructive successor to simazine is "polyquat," a polyquaternary ammonium compound: (poly [oxyethylene (dimethyliminio) ethylene (dimethyliminio) ethylene dichloride]), with an E.P.A. est. no. 8709-PA-1. Polyquat is widely used as a swimming-pool algicide and in clearing industrial cooling-water systems. It is a surfactant that lowers the surface tension of the water and "wets" algal cell walls, splitting their delicate membranes and spilling the cell contents. Polyquat is manufactured by Buckman Labs, Memphis TN, and repackaged for the aquarium/pond market.
After testing their polyquat, "Pond Care AlgaeFix," with pond plants, including Cabomba and "Egeria" (Elodea), Aquarium Pharmaceuticals marketed "AlgaeFix" for aquaria in 2001. They warn you, at their website, not to use AlgaeFix with any crustacea you care about, like freshwater shrimp and crayfish. Crustacea that you don't care about, copepods especially, will also be decimated by polyquat: if your algicide kills off your algae-eating plankton, can it be a good thing in the long run? Swimming pool owners who require brilliant clarity keep their water "dosed up" with polyquat. "One treatment with PolyQuat can last months," says the PoolStore website approvingly; one dose of polyquat in an aquarium may also not degrade for months, and in an aquarium, that's a long long time. Even an amateur has reservations about adding any surfactant to aquarium water. And not every professional would agree that polyquat is harmless to fish. "This pesticide is toxic to fish," warns the Nu-Calgon Material Safety Data Sheet. "Keep out of lakes, streams or ponds." ...I'd add "or aquaria," but you know how skeptical I am...
Swimming pool owners eliminate the dead algae with either a shock dose of chlorine or some other oxidizer to break them down. They may then use a flocculant "water clarifier" to clump them together to be caught in the filter.
Glutaraldehyde. About 2005 some advanced aquatic plant enthusiasts began dosing planted tanks with glutaraldehyde CH2(CH2CHO)2, a pungent and toxic disinfectant and preservative that in a stronger solution will kill the virus that causes warts. In a polymerized form, its bioavailable carbon (the C in its formula) serves as a fertilizer for aquatic plants and suppresses algae. Apparently it's a component of Seachem's Flourish Excel. Overdosed, above 1 ppm, it can severely stress aquatic mosses and vascular plants. Its enthusiasts, all too casually doubling the highest recommended dosing, or spritzing and painting rocks and hardscape with stronger solutions, and reporting that dosing with glutaldehyde killed snails, do note that some cloudy water may ensue, whether from bacterial die-off or from knocking back the plankton. I mention this method simply because some aquarists are using it.
Flocculants and green water. Flocculants appeal to your worst "nuke it!" instincts. A flocculant is a substance that makes colloidal silt and organic particulates, including single-cell algae and even bacteria, clump together in "flocs" and precipitate out of the water column.
Flocculants are an aspect of chemical filtration. Typical "clear water" flocculating products often take a synthetic polymer built of a long chain that bears many positively-charged sites and combine it with a polyvalent (multiply charged), non-toxic metal salt, such as alum (aluminum sulfate). Kordon gives an unbiased account of how their flocculant "water clarifier" Trans-Clear works, at their website.
It would be so nice to be able to unconditionally recommend a flocculant. Why can't I? Overdosing with a flocculant water clarifier can temporarily cloud the water with colloidal particles, but this is more an issue for the aquarist than for the fish, which are unharmed. But the flocculants carry strong positive charges, which unselectively bind with negatively-charged sites. Negative charges on small particles make them mutually repellant and help keep them in circulation. The cellular membranes of algae cells also carry negative charges, so the flocculant works like a charm! But mucus-covered gill surfaces carry negative charges too; they can't bind to the flocculant, so if you overdose, the flocculent may bind to them, gumming together the delicate gill filaments. If you eschew aloe vera as a stifling gill glue, you'd also be cautious when using a flocculent. Small fishes are rumored to have been directly smothered by overdosing with flocculants. I'm convinced flocculants are stressful. But the basic point is that both poisons and flocculants are piecemeal panic measures; if you haven't got conditions in the aquarium balanced, algae will be back.