BioWare has announced via Twitter that Mass Effect 3 will have a demo. The ME3 demo will feature playable sections for single players and multiplayer co-op. You'll be able to download the demo in January 2012, 2 months before its March 6 release date.
"We'll have a pre-release #ME3 demo in January 2012! There will be a single player and multiplayer section, so get excited for the New Year!"
My New Year's resolution? To save the galaxy.