Mathcad – the easiest to learn and use, with formatting approaching word processor level for report-writing, and much of Maple incorporated.
O-Matrix An excellent affordable tool that has an add-on to accept Matlab m-files.
Mathematica By Wolfram – the premiere high-level analysis and modeling tool.
Matlab The oldest and a standard in many facilities, now with Simulink and other tools.
Maple The people who brought algebraic manipulation to the mainstream, sill the leaders, in a full-featured modeling and analysis environment.
http://www.derive.com/ Derive, from Texas Instruments
http://www.pims.math.ca/knotplot Knotplot, for topological visualization of knots
http://www.mupad.com/ MuPad, algebraic manipulation and visualization
http://www.cs.sunysb.edu/~algorith/implement/pari/implement.shtml Pari for number theory
http://www.uni-koeln.de/REDUCE Reduce, a computer algebra system
http://www.geometrygames.org/SnapPea/index.html SnapPea; see link for information; if the move it, search on SnapPea
http://www.insightful.com/ SPlus, a data anaysis and statistics environment