as stated Gimp is by far the best free alternative. However if you just need to remove redeye and simple touchup to photos then you might check out Google's picassa also.
I tried Gimp, but didn't like it. I couldn't figure out all the windows it made. Personally, I felt it was aptly named, but some people swear by it. Maybe I didn't give it enough of a chance. I like Paint.NET It's free and it's easy to use.