What video game sequel(s) do you feel were the biggest improvement over their immediate predecessors?

Street Fighter II. The first one was clunky and is now borderline unplayable, but the second one caused a massive change in the way that fighting games were played, and has many fans to this day.

Uncharted 2

Couldn't have said it better. This, to me, is by far the biggest gap.

Super Smash Bros. to Melee is a big jump too.

Jak 3

Probably Metal Gear Solid 2: Sons of Liberty. It basically took every single element featured in the previous game and expanded over it with such magnificent care for detail and polish, it's insane to think how did they managed to make all that. Improved third-person/first-person mechanics, the ability to lean on covers, hold-ups, passive/agressive enemy AI, radio mechanics, bodies that obstructed your movement, interactive enviroment, bazillion of easter eggs, references and comments, new and improved arsenal (even if the Nikita is a glorified puzzle weapon this time), two completely different scenarios, a hundred VR missions, and on top of all, a storyline that would serve as the franchise's pivotal structure for later sequels to come.

Over all that, there's also the meta-narrative about the postmodern deconstruction of a videogame sequel. So yeah, MGS2 is my choice here.

Mega Man II
Street Fighter II
Kirby's Adventure
Super Mario Bros. 3 (considering lost levels as its predecessor)
Devil May Cry 3
Mass Effect 2
Paper Mario TTYD

Dune 2
Silent Hill 2
AC2

Assassin's Creed II. Better than the original in every conceivable way. Uncharted 2, Smash Melee, Pokemon Gold/Silver. Those are the ones off the top of my head.

Super Smash Bros. Melee.