Graphmatica

Graphmatica is a small program designed for students and teachers of Mathematics. With it, you can graph your own equation just typing it over a text field and pressing enter.

Graphmatica is very easy-to-use and have a lot of interesting options. You can easily switch the graph paper (ex. to show polar coordinates instead of the standard x-y graph). Moreover you can change any graph color: the background, grids, and function line colors can be altered to easily match your needs.
Looking at the math features, after you draw a line over the graph you can easily (I mean 1-click) find derivatives for such equation. The same occurs with numerical integrations: just select the area and the program makes the rest.
Personally, I found this program very interesting. The only drawback is that you could use it just for 30 days, after that you have to pay for it. Another issue to mention is that you have no help at all when typing the equations. If you misspelled something, then you get just an error message. It will be crucial to read carefully the help file before to start using it seriously.