NOTE: This solution "burns the subtitles" into the video, so that every viewer of the video will be forced to see them.
Use the libass library (make sure your ffmpeg install has the library in the configuration --enable-libass).
First convert the subtitles to .ass format:
ffmpeg -i subtitles.srt subtitles.ass
Then add them using a video filter:
ffmpeg -i mymovie.mp4 -vf ass=subtitles.ass mysubtitledmovie.mp4
