To me sequels only seem a good idea if you originally plan the story to span more than one game.
After playing the original Halo recently, the ending makes me feel that Bungie did NOT entirely have a trilogy planned, but more that they had the idea in their heads if it ever did very well. (which, as we all know, it did)
However i was one of the few people who didn't really enjoy Halo 2 or 3. The story tried too hard to maintain the original's mysteriousness, but instead just made things feel like they weren't being explained when they very well could have been.
There's a difference between the feeling Halo gave me of 'I wonder what the forerunners were?' to the feeling Halo 3 gave me of 'Bungie, just tell us who the **** the forerunners are!' (new to these forums, not entirely sure if swearing is allowed, haha)
to me the original Halo wrapped up it's own little story and just implied that the war would continue, which is fine by me. Hell any World War 2-era game that does NOT end with you actually ending the war is the same thing, we only play more famous battles and afterwards the war continues (and we are often told as to how it ended after the events of the game)
I don't mean to rat on halo, i do enjoy the series, i just don't find 2 or 3 anywhere near as ominous and cool as the original, but to me it's also the best example of how you should make sure the ENTIRE story is planned.
A better example is, not so much Half-Life 1-2, but Half-Life 2 and it's episodes. They flow so smoothly together as one story that they really feel that THAT is how a sequel should be done.
Ok, after all that gabbing let me sum up... i feel the only games that deserve sequels are the ones that have one planned out ANYWAY. I feel sequels are a bad idea at re-starting a franchise, UNLESS they don't actually play out an advancement on the same story, but just create new stories in the same world. A bit like the Oddworld games, but it's a shame they gave up making games due to poor sales.