Any infinity (countable is the "smallest" infinity, I think?). I was inspired to this question by reading "down and out in the magic kingdom", where people live forever , but occasionally get bored and commit suicide. So I wonder if in theory, there would be enough new stuff to discover to make it interesting to live forver.
In one of Larry Niven's novels, an AI who was a recording of a human mind discovered this trick on a long interstellar flight:
When things get really boring, arrange to have all references to the concept of "boredom" wiped from your memory. Then, when things get boring the next time, it's a novel experience!