FOOK2 - adds TONS of new weapons and various game tweaks;
FWE - combines a whole to of useful smaller mods into one package and rmps up the difficulty to "FUCK THIS SHIT" level. Persnally - get the ReadMe for that mod, and download all the smaller mods by themselves - this way you get awesomeness, but no the terribad gameplay. Smaller mods include Sprint Mod, Bullet Time mod, Grenade Hotkey mod and tons of others.;
GreenER World - Not Green World, mind you. Both are similar in that they both add a lot of vegetation, like green trees and stuff, to the world, making it feel more alive GreenER World just looks better;
Fellout - removes the green tint from the game, and makes it look MUCH better. Just get a good nightvision mod with it, because the nights are dark as hell (at least they were the last time I checked);
More Where The came From - or something like that. Let's you expand GNR with more music, or with music of your choise (up to 100 tracks);
BABE - body replacer, the best I've seen. Replaces female bodies and clothes to make them look good. Comes with regular and butt-naked versions;
PuceMoose - not a mod, but a modder. He makes AWESOME qurst mods. He had 3 or 4 the last time I chacked, and they wee all AWESOME;
Also, you'll need a few programs to run the mods:
FOMM - Fallout Mod Manager. Helps you manage (imagine that, huh?) your mods. And it had a built-in Archive Invalidation, which you'll need to install mods properly;
FOSE - Fallout Script Extender. While not required, it makes a lot of mods function better, by adding (or "extending", if you will) new scripts. Highly recommended. It disabled GFWL, mind you, so if you didn't get all the achievement yet (if you even care about that), now would be the time to do so.
That's all I can remember that goes under "essential" section. I have like 80 more installed, but I'm not near my PC right now, so I can't list them all...
PS. Also, what the others have listed is hardly essential.