Convert animated gif to mp4
You can use two programs, Imagemagick's convert command and ffmpeg, to do this.
convert -coalesce animation.gif frames%04d.png

Then convert the pngs to a movie:
ffmpeg -r 10 -i frames%04d.png -vcodec mjpeg -y movie.mp4

For a GUI, it would not gain you much convenience, but I know QuickTime Pro (you might have to get the old version) will convert a stack of sequential images into an animation. I don't know if it will read the GIF properly.
Edit: see @Henry's answer for another codec using h264. In short, for a more modern compression scheme on the movie, use -vcodec h264 instead