We looked at Pixlr in class. Pixlr Express might have some uses, but the Pixlr Editor is probably as close as you can get to something like Photoshop in an online app.
This all might be overkill for many school projects, but still might be fun to mess around with, if you like that sort of thing. You can probably find some Pixlr-specific tutorials online if you poke around a bit. Here's one set, for instance.
If you'd like to look at other options, SumoPaint is another Photoshop-like editor that works in a browser. It's been around for quite a while, and is actually more Photoshoppy than Pixlr. Like all web apps, though, it can be clunky, slow, and unresponsive at times. So can Pixlr.
For something faster, you could download the GIMP, a free, open-source program that's been around for many years. There are plenty of tutorials around that are GIMP-specific.
Mac users, if you've got some cash to spend, Pixelmator is a slick $30 image editor on a par with Photoshop. (I've owned a copy for a long time, but don't use it much, because I'm so much faster in Photoshop!)
Windows folks, is there anything comparable out there? What other image editors have you used, online or otherwise?