Lots of 'must have' mods in my humble opinion. Does rather depend on if you play the hardcore version of the game, too.
Fallout Mod Manager or 'FOMM'. This makes every mod amazingly easy to install and I cannot recommend it enough. In fact, I'm pretty sure some mods require it. Have a look through
these excellent lists for the 'top 100' mods and so on.
Anyway, a selection of my MUST HAVES:
PerkEveryLevel - for some reason in vanilla it's every other level or something annoying.
UndergroundHideout - a simple, sprawling home packed full of easy to use features. I love the displays and being able to sort all your ammo, crafting supplies, aid, clothes at the press of a button - and then being able to display them all, too!
Centered 3rd Person Camera - the vanilla camera angle annoyed me.
Fellout - darker nights, nicer skies and more. The kind of thing you think you can do without until you install it! Get CateyeGogglesOnly, too as they will help you during the nights.
Blackwolf Backpacks - really handy and they look nice.
Weapon Mods Expanded - does what it says on the tin. Nice for more experienced player to tinker with weapons.
New Vegas Bounties - adds LOADS of new content.
101 posters and billboards - brightens up the wasteland no end
The 3 NV Interiors mods - they add a lot more enterable buildings. I don't know about you guys but I hate finding a building boarded up!
UrgeWasterScarf - adds two shemaghs that look great and really compliment a lot of outfits. They also cover up that awful 'neck seam'.
A World of Pain - adds more content to kill.
Dimonized Type 3 - replaces the vanilla version with a much better body - many other mods need this.
Narrowed Should Body Meshes - much better shoulders for Type 3.
New Vegas Script Extender and Archive Invalidation - necessary for most mods.
Weapon Retexture Project - makes the guns look MUCH better.
Beware of Girl Type 3 - makes the Type 3 bodies look nicer.
The above might not list the actual names - this is just off the top of my head. ALso, there are way more 'essential mods' but a lot depends on your play style. You can find them all at Fallout New Vegas Nexus.