Funk Engine said:
Well, we don't really "need" anything but food and shelter, but I think the OP really was asking what games should have a sequel according to the community. Ah yes, language, mother of all misunderstandings.
While I agree that sequels shouldn't be done without sense or just for the sake of establishing a franchise (why hello there, BioShock), I think it's too narrow to only allow sequels if the story allows it.
First there are games like Portal 2. I agree with Yahtzee that Portal's fun comes from the puzzles, the story is a nice background, but it's still a background, so I didn't mind the sequel retconning and twisting stuff just so it could happen.
Those are the games where story plays a secondary or even altogether forgettable role and you want a sequel because of the overall gameplay.
Then there are games that do not necessarily add to the canon or rewrite history forever, but flesh out a Constructed World by letting us view the world from a different, interesting perspective. Its timeline may or may not overlap with the main one. I think Crysis: Warhead did the latter, but I haven't played it, so I can't name that as a confirmed example. I did play Homeworld: Cataclysm tho. It's set after the first game (Homeworld 1) that told a completely round story from beginning to end. Homeworld: Cataclysm's story is not mentioned once in the next sequel (Homeworld 2), but it let us view how history developed in general after the first game's achievements and how life is like for a small, weak clan (as opposed to the entire race you're commanding in Homeworld 1).
It's a sequel that isn't *necessary*, but fleshed out the world and brought some new toys in gameplay, thus it didn't feel like stagnant "franchise stretching" at all. Since its story is completely different from the original, as is the vast majority of the units, it's not exactly "more of the same" either, tho there are certainly characteristic similarities.
TL;DR
So as I see it there are simply interesting and uninteresting sequels, those that can bring enough new things to the table to be interesting on their own, without the strength of its successor, and then there are the boring sequels that don't add enough new and just feel like stretching and a waste of creative minds. Nintendo's struggling with this.
OT
Rayman. The Jump & Run, not the bunny minigame collection.