These steps are only for the GOG version of Fallout New Vegas because it comes with Game For Windows Live already disabled and with the Large Address Aware fix incorporated that allows the game to use more than 4 GB of your system memory. I don't use the Steam version and can't offer support for it.

I would also recommend, though I don't think it's necessary, to make sure you have the latest Fallout New Vegas script extender installed. http://nvse.silverlock.org/

1. - Make a clean install of the GOG version of Fallout New Vegas.
2. - (OPTIONAL) install the ENB of your choice following the authors instructions.
3. - Go to your "Windows/System 32" folder and COPY (do not cut or you may cause issues) a file called "DXGI.DLL"
4. - Now go to the game folder for Fallout New Vegas wherever you installed GOG and/or the game. This is the  main Fallout New Vegas folder, not the data folder.
5. - Paste "DXGI.DLL" to this folder and overwrite if prompted.
6. - The game should launch normally. 

You may have to do this again in the future if the game stops running properly. I've had to update it twice myself, but this fix should continue to work for now. I hope this helped you guys continue to enjoy these great games.

EDIT: I've been informed that while this is an issue for Fallout 3, it may not be a problem for Fallout New Vegas. For now I'll leave this up but if it turns out to be not needed I'll remove it in a couple weeks and thank you everyone for the info and feedback!