I found AI behaviour that could use a bit of improvement here:
This is my empire at turn 213. Notice something amiss? Despite there being five religions in the game for quite some time, none of my cities (barring two border cities near Egypt) has any religion. In fact this was the case for another 80 or so turns. I was the only player without a religion in this game (Byzantium got the fifth), and despite having nearly all the religion-focused leaders (Gandhi, Boudicca, Theodora), none of them has bothered so far as to send a missionary to these large, irreligious cities. Instead, Gandhi is more focused on converting Theodora's cities, which already have a religion and which is earning him diplomatic demerits.
This is suboptimal on the part of the AI because spreading your religion to large neutral cities (in particular, being the first one to do so) gives disproportionate benefits, depending on what your founder belief is, and no diplomatic repercussions at all.