If you haven't already, you should try Sage.
Advantages:
- Open source.
- Includes many different packages (including GAP, Maxima, Singular, PARI/GP, and R, just to name a few), and provides a common interface for them.
- Has a built-in Python interpreter.
- You can install it on a server and allow people to run it remotely, through a web browser.
- Is still actively being developed.
(Possible) DisadvantagesDisadvantage:
- No native Windows version. (You can still run it on Windows, but you have to run it under a virtual machine. This is fairly straightforward, though.)

