What I like to do is keep my completed game for reference - to see what the various puzzles and collectibles look like when they are complete.
I make sure the tribe is ok and self sufficient (with doctors, parents, farmers etc.), maybe check back on them every so often.
Then start new games and play them differently - like buying the techs in different orders, seeing how long I can go before collecting food, maybe concentrating on breeding and building instead of doing the puzzles all right away, making a tribe with one colour hair....
There are countless ways to play again and make it new. I've got all three games and play them over and over again. Just because you've completed it once doesn't mean that's it and you need to move on!