Pikmin 2 hands down. 80% better than the original imo, even taking the originals extra creativity and innovation into account. SMB3 for nes is also a great sequel. I am not sure if it is considered a sequel, but Super Mario World is also fantastic. Mario party 2 is also a fantastic sequal, as is Super Smash brothers melee. Banjo Tooie was a marvelous sequal that was almost as good as the amazing original. I am hopeful that fable 2 will be a great sequal...

Final Fantasy VI, Earthbound, Half-Life 2, Call of Duty 4, Resident Evil 4.

Shenmue 2

Metal Gear Solid 3 

Metal Gear Solid(it is the third in the seris)

yeah if you count it like that it is one of the best sequels

Super Mario Bros. 3
Super Mario 64
Super Mario Galaxy
Zelda: A Link to the Past
Zelda: Ocarina of Time
Zelda: Majora's Mask
Zelda: Wind Waker
Zelda: Twilight Princess
Final Fantasy VI
Final Fantasy VII
GTA SA
Super Metroid
Metroid Prime
Call of Duty 4
Half Life 2
Warcraft 3
Super Smash Bros. Melee
Super Smash Bros. Brawl
Kingdom Hearts 2
Metal Gear Solid
Starcraft 2 (i got to play it, beats original in every way)

Resident Evil 4 

^those are alot of best sequels

if we are talking about direct sequels (right after the previously released one)
SMB3, GTA3, Diablo 2, Warcraft 3, Smash Melee, Paper Mario 2

i'd say mario 64, but i don't consider it a direct sequel to the 2d games