Bethesda's Pete Hines tells Kotaku that the company is "currently working on releasing patches/updates as quickly as possible for Fallout: New Vegas, for all platforms."
One such bug, which leads to some weird animation with the very first character you encounter in the game, is particularly amusing. It has been documented in a YouTube video, which can be found below.
The animation bug seen above was said to have been squashed, pre-release, by producer Jason Bergman. If you're on the PC version, try re-verifying your game files through Steam, which may fix the issue.
Until the patch hits, let us know what bugs or issues you're facing with Fallout: New Vegas. I started playing it last night on PC and thankfully, haven't hit anything that affected my gameplay experience yet.