BioWare announced a playable demo for Mass Effect 3 on February 14th.

Here's the relevant portion of the FAQ on the official site :

"What content will be included in the Mass Effect 3 demo?

There are two sections in the Mass Effect 3 demo, both included as part of a single download: The single player section includes 2 areas: the opening level featuring the Reaper attack on Earth, and a level further into the game where Shepard travels to an alien home world to seek their assistance in the war effort. This will be approximately 1 to 2 hours of content.The co-op multiplayer section includes 2 maps: Slum and Noveria. This section will be open to players who have qualified for the early multiplayer access as of Feb 14, and will then open up to all players on Feb 17.

How do I qualify to play the co-op multiplayer section before Feb 17?

The early access program for the demo’s multiplayer section begins on Feb 14, 2012To gain access to multiplayer in the demo any time between Feb 14 and when it opens up for everyone on Feb 17, a player must have met one of the following criteria: Own Battlefield 3 and have activated BF3’s Online Pass. Logging into the demo using the EA Origin Account linked to that Online Pass will automatically unlock the multiplayer section of the demo. Note that you do not have to enter a code anywhere – if you have activated your BF3 online pass, the multiplayer section of the demo will be unlocked for you when the demo goes live. Participate in an early access program that will be announced on Feb 7, 2012 – watch this site for more details."