What is The Facebook Font?
The Facebook font is a custom font created by a font designer named Joe Kral.
The closest font is probably Klavika Bold which is a commercial font.
UPDATE! Facebook has made subtle changes to their logo in 2015. The "F" and "k" still look similar but the other letters have changed (Note the letter "a"). We don't know of a font to reproduce the logo exactly, so you will have to work with what we have below.

Purchase the Facebook font here:
An artist on DeviantArt, Bogdan Balațchi, created a free font based on the Facebook logo. Its license doesn't allow it to be shared, so we no longer offer a download here.
What is the font used in the body text of the Facebook website?
Lucida Sans
Note: Lucida is a commercial font family, so we no longer offer it as a download. Lucida Grande comes installed on Macs.