You can play DIVX AVI files on the PS3. I have not tried playing them from a burned DVD. I used to just hook up an external hard drive via USB, but now I just stream them from my computer using Windows Media Player 11.
There are other file types that the PS3 will play, but all my stuff is in AVI format. Now it will not play all AVI files, but Super Video Converter will convert to PS3 format as well.
I am really loving the PS3 as a media player. I hardly play games at all on it, but I do play Blu-ray movies and AVI files. It handles photo's really well too.
One thing to note...If you hook up a USB hard drive, you would think that when you select it in the menu, it would show the files. However, it does not, it will say no files found. You have to click the triangle button for options, then select display to see them