I saw a thread recently on biggest drop in quality, so let's go in the opposite direction, biggest improvement. 

IMO, Metroid Prime 2. It improved on Prime in every way to me. Better more original art, very intriguing world, bigger scope, much more difficult, cooler powerups, improved graphics, and best music in the series. I think it is the best game in the series.

Super Mario Galaxy 2- Improved upon the original in every way.

Borderlands 2- I didn't love the original, but I liked it, the second one was much better.

Pikmin 2- More exploration, more pikmin. 

Uncharted 2- Uncharted 1 was a good game, but U2 blew it out of the water. A truly amazing game.

What are some of yours?

Umm the biggest drop quality thread was inspired by a biggest imporved one.....

So you were inspired by the thread that was inspired by the same thread you're making right now

uncharted 2
killzone 2
call of duty modern warfare
Need for speed underground
assassins creed 2

Batman... the second games is way better than the first.
LittleBigPlanet... the second is the definitive game.

Halo 3 to Halo 4

As I said there was already this thread lemme find it.

http://gamrconnect.vgchartz.com/thread.php?id=154279&page=2#9

same name too.

F-Zero GX
Super Smash Bros. Melee
Sonic Adventure 2
Grand Theft Auto 3
Mario Party 3
Banjo-Tooie
Pokémon Gold/Silver version

In everything except the Multiplayer... that's the same point I don't give this edge to Killzone 3... the Multiplayer is weak than the previous one.