Are there robust alternatives to Photoshop that are either cheap or free?

GIMP perhaps?

Paint.NET
Great freeware. :)

You can also try GIMPshop, which is a GIMP modification. It gives a Photoshopish interface to the software.

Keep in mind that GIMPshop is based on an older version of GIMP (2.2 vs 2.6)

*cough*
Yes, there are a few. Which one is your best option depends on what you need it for.

Start>Run>mspaint.exe
Less flippantly, Photoshop Elements is pretty good, and substantially cheaper than full photoshop. Try the demo, it might do everything you want and not be shitty, slow & messy like GIMP
You're a student aren't you lowy? Have a look for student discounts, you might get the full version of photoshop for the price of 2-3 games rather than 20-30

GIMP is pretty powerful, in some ways more than photoshop, but also missing some important elements that photoshop has. Interface is a pain to learn if you know photoshop (but then so is photoshop)
Paint.NET is a great lightweight photo editor, which starts up much faster than PS/Gimp so I use a lot for day to day stuff, but it's not really in the same class for professional stuff.
There are a lot of online free ones that sometimes have surprisingly advanced features. Photoshop online is basic but polished, as is picknik, Aviary has more advanced tools, and there are lots of others too.
Pain Shop Pro is pretty powerful, and a mid level in terms of things like features and price. Might be worth checking out in addition to elements.

Also worth taking a look at eBay. I got a full copy of CS2 as bankrupt stock for a lot, lot less than it should have cost. This was back when CS3 had just been released. Given the recession, I'd imagine there should still be plenty more where that came from.

I have absolutely no idea how I completely missed this thread.
Thanks for all the recommendations. I'll have a closer look at some of the suggestions later tonight.

On the mac, there's Pixelmator.

It depends on what you were using Photoshop for.
If you were just doing image editing, MS Paint or Paint.net will more than be enough.
GIMP is pretty comparable, but it has a drastically different (linuxy, yuck :p) interface.
That being said, for everything I do (image cropping, making textures for models, etc) Paint.net does the trick. The main things it is lacking are most of the fancy filters. But if you never knew how to use those in the first place...

Just remember that Photoshop is a multi-purpose graphics workhorse. Most free programs are more focussed on one particular task. So, depending on what you need to do, you may need several freebie apps cover the spread.

Which is awesome.

That is true but conversely there's a reasonable chance of paying for a LOT of stuff you just fon't need unless you're at least a semi professional level photographer