Some of these have been mentioned already. Oh well.
Sawyers mod. Must have.
NVinteriors adds so much it would be a crime not to use it. I always wanted to explore those train cars and some of those boarded up building. Now you can!
DFB Random Encounters adds a few spawn points with enemies of your choosing. Enclave is off by default thank God. It's one of those mods that is essential for me, simply because I know where every single enemy is in the vanilla game, and it gets boring after awhile without some variety.
Try Performance of the Gods if your computer is real crappy. It will speed things up.
http://newvegas.nexusmods.com/mods/45475
Darnified UI is a must, to get rid of those ugly ass fonts. Mtui is a nice alternative.
Pipboy 2500 is the perfect mix of nostalgia and improvements. Lots of skins for the readius mods too.
Centered 3rd person camera does just what it says. You can even zoom out and almost trick yourself into believing it is Fallout 2...almost.
Weapon Mods Expanded allows you to mod unique weapons, adds a few mods, and works quite well with Project Nevada. It never leaves my load order.
Personally, I like making my raider chicks look like wasteland sluts with genitalia piercings, titties hanging out, and other such perversions. For instance, it bothered me in Gomorrah how the whores didn't dress like whores. I fixed that. Just a minor thing that bugged me.
Bottle that Water mod is great too. It does what it says.
KDE Portable Camp Stuff is worth checking out too. It's hard to describe, but you can basically drop various things such as stairs, beds, walls, campfires, reloading benches, to make your own campsite or home.
http://newvegas.nexusmods.com/mods/46195
I always use a backpack mod too because, well, it makes sense in the wasteland to have something to carry your shit in. Shit needs to be carried people. It doesn't magically disappear. Stupid game designers j/k...
Tfh Rugged Race. Make your men look like MEN. I just started a playthrough with this, and I will NEVER play without it again. You want to look like Clint Eastwood? Now you can.
http://newvegas.nexusmods.com/mods/48629
Fake fullscreen. Improves stability. Now you can alt tab without crashing.
http://newvegas.nexusmods.com/mods/41381
4gbextender. Use it. Love it. You need it.
http://newvegas.nexusmods.com/mods/35262
Casino heist. Adds lots of caps to the casinos since they didn't have any for you to rob.
http://newvegas.nexusmods.com/mods/41847
Arwens realism tweaks is one of those acquired tastes. It makes so many changes to the game, it's like a whole new game at times. You have to have a knife to skin stuff, you must worry about bacteria infections, strain from carrying too much gear (or you will pass out), and if one of your limbs gets crippled you can't use two handed weapons at all. So many changes that I can't list them all. Just read it to see if you want it.
http://newvegas.nexusmods.com/mods/34759
I don't use Nevada Skies anymore since it bogs my system down and can be a bit glitchy at times. I don't look at the sky that much anyway. It's pretty though. The alternative to that one is Project Reality.