Here are the mods I use:
Darnified UI
Never properly finished sadly, but still the best UI replacer in my opinion. Sharp and functional.
ADAM - A Definitive Armor Mod
Really nice High res retextures of all the NCR armour. Sticks to canon and makes the Ranger armour in particular look a lot cooler and more like the box artwork version.
Populated Casinos
Transforms the casinos from deserted ghost towns to thriving, packed places. The only downside is that is crams too many NPCs into the Atomic Wrangler, but the rest are pefect.
Refined Casino People and Suits
This obliquely named mod corrects the suit colours of some of the strip factions to be consistent with their lore. Clearly a
very important mod that is essential for MY IMMERSION.
Nevada Skies - Weather Effects BETA and URWLified
Weather and colouration mod that makes things look a lot nicer and adds some interesting dynamic weather effects. Also makes things much darker at night which I prefer.
Inofficial Community patch
Can't find a link for this. Controversy time - I don't like ANY of the unofficial patches for this game, as they ALL add in all kinds of stupid feature creep shit that shouldn't be in a bug fix mod, they all introduce loads of new bugs (try starting Honest Hearts with the latest Mission Mojave!), mangle NPCs names/looks for no apparent reason, and misunderstand Obsidian's deliberate game design decisions (stop making Doc Mitchell's stuff owned! It's purposefully there for new players to take). This patch still does some of those things, but was made before most of the more egregious stuff of the other mods was added, so it MOSTLY fixes stuff that needed to be fixed.
NMC's Texture Pack
Replaces the game textures with super high res ones that look much better. Make sure you use the 4GB executable with this to mitigate the extra crashes that will result due to memory issues. Still worth it despite this.
Delay DLC
Stops you getting bombarded by a million and one pop ups on game start if you have DLC installed, and also makes the start of those quests a lot more coherent and sensible.
Courier's Stash selector
Stops the game dumping tons of items on you at game start, and makes it easier to make your own pre-game history for your character.
Weapon Retexture Project - WRP
Beautifully detailed high res weapon skins that look a lot nicer than the vanilla ones. Most vanilla weapons redone now as well.
Lucky 38 Map Marker
Simple mod that makes the Strip much less frustrating to get to, and makes using the Lucky 38 as your HQ much more viable.
ENBSeries for FNV
Graphics enhancer that completely transforms FNV and makes it look like something half modern. Takes a while to get going well, and really needs some technical knowledge to do so, but worth it. Check the official forums for lots of stunning settings from others. I wouldn't recommend this for first time players though, as it breaks a few ingame visual effects that can be confusing/annoying if you don't know what is/where they are supposed to happen.
Stuff what I done. I made all the mods below, so I'm biased that I think they're good/essential. They might actually suck!
The Strip Open
When I first got New Vegas I really didn't like the Strip. The gates were just plain bizarre, destroying the entire visual aesthetic of the place and making it insanely frustrating to navigate. Then I saw the E3 footage of it and how it was supposed to be before they had to split it up for the console versions. When this mod came out it was revelatory and completely changed the strip from a pain in the arse to the jewel in the game's crown. Unfortunately the guy who made it didn't have time to finish the mod and it was abandoned for a year, with loads of bugs and vanilla game stuff not working. So I learnt how to mod, and fixed it up. Now it integrates perfectly with the vanilla game, and even restores a few missing things like the Second Tops Promoter and his previously unseen dialogue. I couldn't even imagine playing this game without this mod.
New Vegas uncut: Freeside Open
The sister mod to the Strip Open. Freeside was also drastically cut down compared to the original plan for the area. Unlike the Strip, most stuff here was just abandoned. 90% of the NPCs were removed, and all the cool little random events with them. This mod makes Freeside an exciting, dangerous, bustling place like NPCs describe is, and restores all the disabled stuff like the gamblers travelling to the strip. It also restores things like Rotface's previously half finished quest, and over 100 lines of dialogue that were variously either removed, or outright broken. Again, I couldn't imagine playing without this. some caveats though: this mod by its very nature makes the game more unstable, and also breaks a lot of other mods due to how it works.
New Vegas Uncut - Outside Bets
This mod restores tons of little cut things. It re-enables the hundered or so NPCs removed by official patches to alleviate console saved game sizes, including things like the horrifically maimed troopers who are supposed to be found in the Forlorn Hope no man's land, and also the random battles that were supposed to take place there between NCR and Legion troops there. It restores several hundred lines of dialogue that don't work due to incorrect dialogue conditions (as an example, in the vanilla game Securitrons literally only say one third of their dialogue due to missing random settings on their dialogue topics). Previously cut events are restored such as watching the Lucky 38 relight after tampering with the El Dorado substation, or the final showdown with Victor after betraying House. People who tell you they are going to go to a new location after their quest (i.e. Emily Ortal, Melissa) now actually do so instead of just being disabled, and other events talked about by NPCs now actually happen (e.g. the NCR now actually have troops at Nelson after the player takes it back for them).