My impression is that convergent evolution is commonplace. Boredom or equivalent algorithms are necessary for any complex learning. Emotions are molded by game theory. Once you have an intelligent social animal the selection pressures relentlessly shape the mind. If I met an alien I wouldn't be surprised if he or she was almost exactly like me in a lot of ways, to the extent that he or she would describe similar drug experiences and have similar archetypes in his or her fiction. In their vast diversity humans vary about as much as biological minds can vary. Think of it as a challenge: I'd be very interested in alien minds that clearly took these considerations into account but still ended up truly bizarre.
On the other hand, the aliens could (for example) have emotions encoding a different game-theoretic strategy, or a different prior over what games it's going to have to play.
One of the most important points raised by the sequences is that not all minds are like humans. In quite a few places, people have discussed minds with slight changes from human minds, which seem altogether different. However, a lot of this discussion has been related to AI, as opposed to minds created by evolution. I'm trying to think of ways that minds which evolved, and are effective enough to start a civilization, could differ from humans'.
Three Worlds Collide would seem like an excellent starting point, but isn't actually very useful. As far as I recall, the Babyeaters might have learned their baby eating habits as a result of societal pressure. The main difference in their society seemed to be the assumption that people who disagreed with you were simply mistaken: this contrasts to humans' tendency to form rival groups, and assume everyone in the rival groups is evil. The Super-Happies had self modified, and so don't provide an example of an evolved mind.
So here are my ideas so far.