Resident Evil 2 and Metal Gear Solid 2 BEST EVAAARRRR!

I guess if by sequel any game added to the franchise can count (whereas normally a sequel would discount games without story lines, but I don't think Smash has a story, GTAII and III don't really connect story-wise, and I haven't played them but I suspect Pokemon games don't really have connecting stories either, so I'm gonna use the definition of great sequel to mean a game improving upon a previous entry to the franchise)

With that in mind:
Timesplitters 2
F-Zero X
Mario Kart: Double Dash
Mario Kart Wii
Pilotwings 64
Endless Ocean 2
Metroid Prime 3
Banjo-Tooie
Half-Life 2
GTAIII and Vice City
LoZ: Majora's Mask, and Windwaker... and I probably would have said Skyward Sword 2 months back, but I'm not sure I rate it above TP anymore.

I tend not to play through whole franchises much, so I haven't played the previous installments of these games, but I suspect if I had I would be able to add them to the above list:
Star Wars Rogue Squadron II
Wave Race: Blue Storm
Resident Evil 4

Actually if I am going to be pedantic I guess both Twilight Princess and Skyward Sword fit in here too due to handheld games coming in between the main console Zeldas

YAY! Someone appreciates the awesomeness that is Mario Kart: Double Dash!! ^_^ You sir have great taste in games.

Tally the results!

Golden Sun: The Lost Age Probably the only game on the list where the sequel isn't noticably better then the first, but hey, this franchise, back on GBA was epic. Best JRPG franchise for handhelds. It's really designed from scratch to play and look amazing on the GBA, similar to Dragon Quest IX, but the graphics seem to be much more optimal

Mario Kart 64 Another amazing 2D-3D transition. Mario Kart 64 is my most played game, and I still prefer it over any other Mario Kart. Best, and most innovative tracks, great item selection, and challenging without being outragous. Best Mario Kart, by FAR!

Mario Party 2 Mario Party 2 fixed all the bugs with Mario Party 1 and improved the game, without adding a ridiculous amount of content, but doing it by quality. How often can that be said for any same generation game? MP2 is the best of the franchise, and it went downhill (hard) from there.

Mass Effect 2 Never seen a sequel with a poorer story play so much better. Amazing pacing, graphics, and just the level of quality and the depth of human conversations is unreal in this game. Real excited for Mass Effect 3

Metroid Prime Let's just say, no other game has ever transitioned from 2D to 3D so majestically. Well, maybe Zelda, but damn... no side scroller ever went this great in 3D, and no shooter ever has been able to mimic that sence of isolation and desparation as this game.

Pokemon Gold/Silver New types, new region, nearly double the pokemon, and to top it all off, the original game was added as a bonus. WOW. Pokemon has never seen such a polished sequal since, and likely never will. I mean, new types and still a great plot. This game managed to hold the fanbase and keep them exceptionally happy. Working on Heartgold now and I just love that I can have every Legendary from both Gen 1 and Gen 2! I hate how new Pokemons not only have Dragon legendaries, but limit you to one legendary per game.

Resident Evil 4 Let's just say Resident Evil 1 is an amazing game, with dated gameplay. Resident Evil 4 is an amazing game with amazing gameplay. RE4 made Resident Evil an amazing singple player experience.

The Legend of Zelda: Majora's Mask Most will object, but I think Majora's Mask is better then Ocarina of Time. A much less generic story, with a pretty bizzarre plot, one that actually gets you to focus since you have a 3 day time limit.

Well I was merely stating it as a vast improvement over the horror that is Mario Kart 64... but yes I still think Double Dash is a great game. (MKWii is better though)

Resident Evil 2,4

Fallout 3

Uncharted 2

LittleBigPlanet 2

inFamous 2

Infamous 2
Mass Effect 2
Super Mario 3
Sonic 2

StarCraft II

Resident Evil 4

GTA: San Andreas

Pokemon Gold/Silver DS

Mario Kart: Double Dash!!

Fallout 3

Resident Evil 4

Suikoden 2

Baldur's Gate 2/ ToB

Warcraft 3

Call of Duty 4

GTA 3 / Vice City / San Andreas

Ms. Pacman is probably the best sequel of all time. It basically the same game as the original, but better in every way. The speed of the game and the AI are infinitely superior. Also, the lipstick and bow are dead sexy!