Games that greatly improved their predecessors IMO:

Silent Hill 2

MGS3

AC2

U2

And I'm sure many others I can't remember right now.

Pikmin 2
Super Mario world
Super Mario Galaxy 2
RE4
Metroid Prime 3
Ratchet and Clank: Going Commando
Mega Man 2
Link to the Past
Guitar Hero 2
Ms. Pac-Man
Star Wars Rogue Squadron 2

Each one of those in my eyes surpassed its predecessor in every way in my view. I would list reasons, but I'm to lazy.

Red Dead Redemption and Killzone 2,

I'm only going to list 2nd installments to a franchise that out-did the first game.

-Resident Evil 2
-Assassin's Creed 2
-Pokemon Gold
-Uncharted 2
-Super Mario Land 2: 6 Golden Coins
-Sonic The Hedgehog 2

Sequels/ Prequels I liked as much or more than their predecessors.

God of War II & III
Jak II & 3
Resistance 3
Gears 2 & 3
Deus Ex: Human Revolution
Forza 3 & 4
Mass Effect 2
Bioshock 2
Oddworld: Abe's Exoddus

Assassins Creed 2 took a decent game play and made it epic and interesting.
Adding in the whole family factor and the more epic storyline made the game great.

Pokemon Gold and Silver were well liked for being pretty much 2 Pokemon games in one. It had two worlds and the new world was great. It had some great battles and likley the most legendary Pokemon battle in history with Red.

Uncharted 2-That game is my favorite game this generation and one of the best games ever made. It improved on the first in every possible way.

Killzone 2- great single-player experience, but even better then the single-player was the amazing online component, a very solid game. (A pity about Killzone 3 in my opinion.)

MW2- much better game than World At War. One of the best COD games this generation.

Hitman 2: Silent Assassin. Improved everything, great game.

Diablo II - I played the first one a lot but this one consumed so much of my time
Uncharted 2 - Soooo good!
Assassin's Creed II - Fixed most of the first title's problems
Resident Evil 4 - Awesome game all around, revitalized the Resident Evil franchise
Super Mario Galaxy 2 - Realized the impossible task of improving on the excellent Super Mario Galaxy!
Legend of Zelda: A Link to the Past - 2D Zelda at it's very best.

~ PIKMIN 2!!!! ^_^

~ Pokemon Ruby/Sapphire
~ Super Mario Galaxy 2
~ I guess you could call Skyward Sword a sequel...
~ ...add Mario Kart 7 to that.

SMB 3- Vastly superior to the first 2
MK Wii- Dominates DD
God of War 2
Killzone 2- Just because the original was flat out bad..