The Gimp

The Gimp (no picture, ironically) is the open-source, free(!) nearest equivalent to Photoshop. I looked at the counter on the Sourceforge server and it said that it had completed 292,151 downloads..this week. Like Photoshop,it's a raster-based image editor; apparently Inkscape and Xara do the vector drawing that Illustrator is known for. Here is the official Gimp site where you can find the appropriate download for your OS and related tutorials and whatnot.