$ ffmpeg -i original_video.avi -qscale [quality] -s [WxH] -ar 22050 converted_video.flv

Join multiple videos:

$ mencoder -oac copy -ovc copy -o joined.avi clip1.avi clip2.avi [...]

Extract a clip from a video:

$ ffmpeg -qscale 1 -acodec mp3 -ab 256k -ss [start time in hh:mm:ss] \
   -t [length in hh:mm:ss] -i video.avi clip.avi 

Dump the audio:

$ mplayer -vc null -vo null -ao pcm -benchmark test.avi 

Grab an image from a video:

$ ffmpeg -i movie.avi -ss [time-in-seconds] -vframes 1 -f image2 frame.jpg

Overlay an image on a video:

$ ffmpeg -i input.avi -vhook '/usr/lib/vhook/imlib2.so -x 0 -y 0 -i overlay.png' output.avi

Encode a Windows-compatible video:

$ mencoder -oac mp3lame -ovc lavc -lavcopts vcodec=msmpeg4v2:vhq:vbitrate=1600
  -o videoout.avi videoin.xxx

with a separate audio file:

$ mencoder -audiofile audiofile.wav -oac mp3lame -ovc lavc
-lavcopts codec=msmpeg4v2:vhq:vbitrate=1600 -o videoout.avi videoin.xxx

There is also a good guide on how use ffmpeg to create FLV videos for posting online here:
http://scott.yang.id.au/2006/07/flash-video-ffmpeg-flowplayer/