Depends on what you plan on designing/doing. Image editing programs like Gimp (free) or Photoshop can also save animated gifs. They usually make use of layers for individual animation frames.
Alternatively, rendering programs like Blender can output gifs, and ffmpeg can convert video files to gifs (I would expect; otherwise there are free programs for that).
/e: Actually, check out http://alternativeto.net/software/adobe-after-effects/
Namely Natron and ButtleOFX, which I will now check out as well.