MPEG is a set of codec standards, and avi is a container format, so what you're saying could be interpreted in many ways...
if you mean you'd like to convert a DVD (MPEG-2) into a smaller format that is stored inside the avi container and playable on your PC (using xvid or H264 as codec for example) then get
Handbrake.
if you want to convert from VCD (MPEG-1) into a smaller format ... etc, then perhaps
avidemux,
VirtualDub, manually using mencoder or using mewig as linked to above.
