Packages are self-contained bundles of Mathematica code that add new functions and other functionality. They are called using the code
Needs["myPackage`"]. Each package uses its own namespace, called Context.
On the Wolfram site one will find standard extra packages as well as quite a few Mathematica applications developed from other sources. There is the mathematica-users.org list and a reference for tensor software on wikipedia.
Geometric algebra, or Clifford algebra, is a powerful mathematical language that contains vector algebra as a subsystem. It has applications across a range of subjects in physics and engineering, and is well suited to symbolic and numeric computations using Mathematica because of its very regular structure.1
Grassmann Algebra Package and Book by John Browne: This includes quite general Clifford algebra functionality.
Symbolic and Numeric Geometric Algebra: This package creates a framework for calculations in the geometric algebra and calculus of three-dimensional space and four-dimensional spacetime is described. Examples are given of its use and application in computational electrodynamics.
Exterior Differential Calculus: This package enables Mathematica to carry out calculations with differential forms. It defines the two basic operations - Exterior Product and Exterior Derivative. There are variations of this package for scalar and matrix and super differential forms.
Also available at: http://library.wolfram.com/infocenter/MathSource/683
Plotting and Graphics Packages
LevelScheme: "Publication-quality scientific figures with Mathematica"
David Park's Presentations Package: This package adds LOTS of custom graphics and other helper functions to Mathematica.
CurvesGraphics: allows for easily placing arrows along curves (in 2D or 3D space) produced by Plot, ParametricPlot, ParametricPlot3D, and ContourPlot and along the solutions to differential equations given by NDSolve; drawing parametric, contour or stream curves or text on a surface in 3D space, or the intersection line of two surfaces, all curves with optional arrows along them.