Simple to use:
ffmpeg -i input_file output_file.extension_of_new_format
like so, to convert a mpeg to swf (Adobe flash format)
bash$ ffmpeg -i video.mpeg output.swf
You can tweak the defaults by adding more parameters. Some that are useful are, bitrate(-b), framerate(-r) and output video size(-s). The last one would scale your video.
So the following:
bash$ ffmpeg -i video.mpeg -b 700k -r 25 -s 580x200 output.swf
would generate a swf that would have a birate of 700kbps, framerate of 25 and a size of 580 into 200 pixels.
If you are targeting a standard, like say dvd video. You can skip typing individual parameters and can use "-target dvd" instead. Check the man pages for more options.