At the Google I/O Conference today, Google unveiled Google TV, software that enables your TV to browse the web and use applications all from your living room. Google TV runs Android, and was demoed using Android 2.2 with Flash support.
What this means for you, is that Google TV will be allow you to play your Facebook games right from your TV. The Google TV system appears to be seamless and allow you to use a bluetooth keyboard and mouse to work out of the box with Google TV.
As of right now, the only thing we know is that Google TV will be built into future televisions as well as be available as a separate box. The idea is to compliment your current set top box, not take it over entirely.
So, yes, you will be able to play your Facebook games very soon on your TV.