My favorite overall may actually be the Green Army from Army Men RTS, simply for the nostalgia value of having an army of little green plastic army men.
Favorites from other games include:
Command & Conquer: GDI
Red Alert: Soviets
Tiberian Sun: Nod
Yuri's Revenge: Yuri
Tiberium Wars: GDI(Marked of Kane if you include Kane's Wrath)
Red Alert 3: Soviets probably, though I do like the Empire's advanced base defense looking like a big gun instead of a weird tower design.
Dawn of War: Orks, though its close between them and the Sisters of Battle.
KKND(1 & 2): Probably the Survivors.
Command & Destroy: Probably the Aliens.
Starcraft(1 & 2): Terrans.
Rise of Nations: Rome in the original version, US when it was added.
Generals: USA. I love all their intel gathering options.
Battle for Middle Earth: Mordor.
Warcraft(All): Orcs.
Empire at War: Consortium, though the Empire is very close.
Galactic Battlegrounds: Though they are all the same, I liked playing as Naboo just for the different look from regular SW factions(and I sure as heck wasnt going to pick Gungans very often).
War Front: Turning Point: Soviets, though all the factions are pretty cool. If only the gameplay was a little smoother.