The High Cost of Doing the Right Thing
"Photoshop" is one of those brand names - like "Kleenex" or "Q-tip" - that has so defined an industry that the word itself has become a generic representation of products in its category. It's even turned into a verb in its own right: "There's some red-eye in that picture I took - I'll have to Photoshop it out," or "that picture's a fake - it's obviously been 'shopped!"
Unlike a box of Kleenex or Q-Tips, though, Photoshop isn't just something you pick up for a few bucks when you need it - unless $600 falls into your definition of "a few bucks", in which case you probably have people who do your Photoshopping for you! High demand coupled with high price has kept Photoshop and other Adobe products consistently in the top 5 of various annual "most pirated applications" lists for many years. Luckily, though, there are a number of free Photoshop alternatives out there that offer most of the features of pricy software; so unless you're an advanced image processing professional for whom the investment is worth it, you don't need to break the bank or the law to get all the image editing power you're likely to need.
For anyone looking for free Photoshop alternatives, there are two primary choices. Both are powerful pieces of software maintained by dedicated groups of passionate developers who subside on donations and day jobs while they dedicate many hours to keeping their applications competitive. Both offer a wide array of drawing and painting tools, image processing and special effects capabilities, and image layering capabilities wrapped in a graphical interface. Both support plugins that allow other developers to add new capabilities to the software that its designers haven't built in. In short, for all but the most demanding of users, either of these applications will meet your image editing needs.
Which to Choose?
If you're running the Mac OS or Linux, the choice is obvious because there's only one: GIMP. For Windows users, the choice is obvious as well - both, because they're both worth having.
I have both programs installed on the PCs I use regularly when I need to manipulate images. I usually gravitate toward Paint.NET because its user interface feels a little cleaner and more responsive than GIMP's, but that's a subjective judgement that others might not share. I recommend experimenting with both and seeing which you prefer. (Note - as of this writing, GIMP 2.8 is in development, which promises a major user interface overhaul.)
Personal preference aside, both programs are worth having. There's always a chance of running into some capability, or plugin, or obvious way to do something that one tool lacks, but the other will fill the gap nicely in a pinch. It's hard to go wrong with either of these applications, but I keep both around just for such scenarios.