Arrhhhhgggg -- I can't believe I neglected to mention Red Dwarf -- of course it was never intended to be a Generation Ship -- but it ended to that the Cat's entire race evolved there, so it definitely has to count...
Do you remember the "Gazpacho Soup" episode? Laugh? I almost bought a round of beers! :-)
I hadn't heard of this -- I just checked and it seems that the action in "Flood" all takes place on Earth -- it's in the sequel "Arc" where the Generation Ship comes into play...
...I've read some of Stephen Baxter's stuff and found it a bit wearing ... on the other hand I did quite like his book "Evolution" (one day I hope to finish it :-)
You wouldn't know it from the title but Flood by Stephen Baxter has some great material about a long-range, long-duration spaceflight and there are kids born on the ship, so I think it qualifies as a generation ship story. The interesting twist is that, although massive planning goes into training and selecting a perfect crew, things don't quite go to plan and the "society" that develops is pretty scary but believable.
Arthur C. Clarke and Gentry Lee wrote three sequels to Rendezvous with Rama - Rama II, The Garden of Rama, and Rama Revealed. These span 3 (or was it 4?) generations of the progeny of the central character, one of a small group who became trapped while exploring the 2nd Rama.
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