New Vegas Stutter Remover [removes stuttering from the game, not that it's name would imply that. If you have the infinite loading screen bug, this combined with the Script Extender fixes it. If you are experiencing crashes, this is the first thing you should try.
Fixes a bunch of things and drastically improves the stability of the game. New Vegas Anti Crash [is the real important one for having a crash-free life. You will need 7-Zip [in order to extract NVSE. It is also needed for most other mods, so you should install it first. New Vegas Script Extender is needed for the below fixes to work. Listed below are the best and most used fixes for loads of issues, including: Hello! New Vegas is a great, but now pretty old game, that didn't run all that well when it came out, and is now only more crashy on modern systems. I’ll keep the below for posterity, or for anyone using older operating systems.
I’d recommend using this guide instead to start off with: UPDATE 2021: This thread now has a lot of older, possibly broken fixes. Read this thread to solve the infinite loading screen/loading screen freeze bug!