For folks who manage Facebook Fan Page accounts, you can now have every post you make on Facebook also post on Twitter by linking the accounts. You can read more about it on the Facebook blog, or sign up to link the accounts at Facebook.com/twitter.
But to those that want to do this to save time, I'd suggest you give it some thought before you link the two accounts. Niala and I have been saying this forever: The two networks are different communities, and sometimes you should customize a post for a certain network.
For example, Twitter only uses 140 characters. Facebook can take more characters. If you post on Facebook, there's the chance that the post on Twitter could be cut off.
And the reverse -- copying a Twitter post into Facebook -- is annoying to Facebookers since Twitter posts are usually filled with @replies and #hashtags... something that only exists in the Twitterverse.
If you link the two accounts, tell us what your experience has been.