These steps are only for the GOG version of Fallout 3 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 3 script extender installed. http://fose.silverlock.org/

1. - Make a clean install of the GOG version of Fallout 3.
2. - (OPTIONAL) install the ENB of your choice following the authors instructions. (this was originally a solution for Midhrastic ENB)
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 3 wherever you installed GOG and/or the game. This is the  main Fallout 3 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: Just a heads up, this was from a thread about Midhrastic ENB working in tandem with Windows 10 and the GOG version of the game. I've been informed that this may not be a problem for other ENB's, and maybe not Fallout New Vegas, but for those having problems I'm going to leave this up.