I used these options to convert to the H.264/AAC .mp4 format for HTML5 playback (I think it may help other guys with this problem in some way):
ffmpeg -i input.flv -vcodec mpeg4 -acodec aac output.mp4
UPDATE
As @LordNeckbeard mentioned, the previous line will produce MPEG-4 Part 2 (back in 2012 that worked somehow, I don’t remember/understand why). Use the libx264 encoder to produce the proper video with H.264/AAC. To test the output file you can just drag it to a browser window and it should playback just fine.
ffmpeg -i input.flv -vcodec libx264 -acodec aac output.mp4