They do go for other ones, but not very often.
The one that is most often different is Democracy vs. Monarchy because for most civs, particularly the ones that don't have the Religion value, it often turns out that the +3 happy everywhere is worth more then the bonuses in the capital - Paradise often uses it. In that same category, every once in a while the Technocracy civic is used, mostly by the Avowers of course, although they usually end up switching out of it after a while. I don't think I have ever seen any use Police State, not even Astrotech who has it as a favorite.
The Syndicate does sometimes switch to Slavery (and then proceeds to whip and draft away half or more of its population, which is not really a good thing).
Capital Ship Doctrine is the most popular in that column, once it is available. The AIs like the +1 happy and tend to build a relatively large number of battleships (which affects the value of it). Some games you may see an AI use Light Ship Doctrine for the entire game. Every once in a blue moon you'll see one switch into Squadron Doctrine for a while, but it is very rare. They do use Pacifism, but usually only until Light becomes available.
I have seen an AI actually use the Green economy. I seem to recall one using it briefly, and there was one that switched to it and stick with it for the rest of the game. The one that stuck with it was a civ that managed to build the wonder to remove all unhappiness in their capital - this is important because the system I added to give some value to the extra population capacity is based entirely on the potential maximum population of the capital due to the happy cap, so having that wonder maxes out the value (extra room on the planets is worthless if you are already at, or over, the happy cap and progresses up to a maximum value as the total population allowed by the happy cap in the capital tops 30).
For 1.8 the specific weights the AIs use when determining the value of some of the civics were tweaked, and some additional benefits were added to a couple of them. This was to get them to be a bit more diverse, but the changes probably didn't go quite far enough.
I don't remember seeing it in the code (didn't look for it), but there seems to be some sort of diplomatic factor in the evaluation. The favorite civics of the strongest civs seem to get more value. Or possibly they just ask the others to switch, and they occasionally do.
Edit: issue moved to a different thread.
