Dunno' if it counts as a faction or not, but I love the Nazi like ideology of the Enclave.

Brotherhood of steel is my favourite faction because I just love seeing them walking around in tin suits

I'd say House, and his Vegas.

Let's face it, this guy is easily superior to anyone in the game when it comes to intelligence - he saved Vegas from nuclear annihilation, sustained himself for two centuries in a machine, and managed to build New Vegas into what it is now despite being completely disabled physically.

He restored civilization to Vegas, turned a bunch of raiders and cannibals into entrepreneurs.
With House's intelligence and the Courier's physical prowess and combat capability, they can form a great alliance. House is pretty much essential for the future of mankind.

Remember, this guy has only recently woken up. A few decades of him in full power could turn New Vegas into a new world superpower, and especially a hub of civilization, advancement and knowledge.

Outcasts in Fallout 3. Their conservative attitude about wastelanders, sense of duty towards the true mission of tech first and play hero later, and their awesome red and black power armor is my kind of group. I agree you can't save every random person you come across in the wasteland, which is why if I could, I would've joined the Outcasts instead of the Brotherhood. But then again, to the Outcast's I'm just a random guy too.

I never really considered the Outcasts to be a favourite faction of mine. I have to agree though, their armor is pretty great.

Definitely "The Kings". I just loved them since the first moment I played the game, since they reminded me a lot the movies "Rebel without cause" and "Grease", two jewels that feature the dreamy 50's and 60's  eras