I decided to make this guide since I've never seen it before. I hope this is useful to some and the mods maybe consider it a sticky somewhere. Anyways there are 2 ways to view animated GIFs on your PSP (until Sony provides this feature in a future firmware update).
Some of you may know this already but you can view them in the browser as follows.
1. Open the browser
2. Go to the URL bar and type in file:/PICTURE/XXX.gif (XXX meaning the name of your picture) Note, however, the GIF can only be up to 2MB.
While this way is less convenient than the first way you don't have a size limit. You can't use the "GIF to AVI" route because the programs that do this change the transparency of the GIF and thus rendering your AVI unconvertible and unrecognizable to any of the PSP video converters. You use Windows Movie Maker because instead of "converting" the file it "transfers it into a movie".
1. Open Window Movie Maker (if you can't find it use the "search" in your Start menu and type it in.)
2. Open or download PSP Video9
3. Import the GIF into WMM and drag it into the first frame of the timeline.
4. Go to File>Save Movie File and select all the defaults.
5. In PSP Video 9 go to Convert>Current Conversion>One-Click Convert and open the movie file.
5. Transfer to the VIDEO folder in your PSP and voila! You just turned your GIF into a movie! To continue the movie like a repeating GIF just turn on the repeat title option.