Is there any way to include an animated GIF directly in either PDFLaTeX or XeLaTeX? I realize the
animate package can include animations in a PDF, but it doesn't support animated GIFs and you have to split them up manually into EPS or PNG files as far as I can tell.
Yes, use the movie15 package (in Latex), which supports GIFs directly. You will need to use a PDF viewer that has the right plugin to supported GIF animations.
Note on media9
The movie15 package has been marked deprecated on CTAN for some time in favour of the media9 package, because media9 uses the better supported approach to embedding media of Adobe's Rich Media Annotations, rather than the old, ad-hoc, plug-in based approach of media15. This has the consequence that building rich media documents in media9 is a more flexible process, supporting several workflows, and the results typically can be displayed with more viewers. However, media9 does not support animated GIFs - the GIFs would have to be converted to a supported format such as FLV or MP4 before embedding.
For animated GIF, package
These are the steps for a 100 frames animated GIF, using package
With the deprecated