I rather like the Choose Religions settings, I find it tends to give the game a more realistic feel if Spain is Christian, China is Confucian or Taoist, and so on.
When I go up a difficulty level, as I just did to Immortal, I like to play with Advanced Start to balance out some of the advantages the AI has. As I get used to the level I wean myself off of AS by lowering the initial points. I usually retain enough points just to get Hunting, a Worker, and a couple of Scouts so as to alleviate the boredom of the initial turns (I usually play my off-line games on Marathon speed).
I also play a lot of my off-line games with the "new random seed" option turned on. This is because I'll often go back several turns to a previous save if a particular strategy didn't work out so I can try something different (since I don't have the benefit of the ALC gang to help me out off-line). While I might do that for strategic purposes, I find the random seed option keeps me honest tactically by not guaranteeing the same results from things like battles, goody huts, and Great People--so, in other words, I'll have a potential price to pay for turning back the clock.
I sometimes play with No Tech Brokering on, usually when I'm at a point where I want a bit of a challenge for my current difficulty level, but I'm not quite ready to move up just yet. NTB closes off two of my commonly-used tactics: one is tech brokering, of course, forcing me to be much more strategic with my tech trading. The other tactic that NTB eliminates is that of selling a tech to the AI for some gold when they nearly have it completed. With NTB on, AI will NOT do this, preferring to reap the benefits of being able to trade the tech in which it has invested so much research. This is one of the few examples I've seen where the AI has been programmed to adapt reasonably well to a custom game setting. (I say reasonably well because there are times when it is more advantageous to get the tech early than to be able to trade it later, but the AI apparently has not been programmed to weigh those benefits against one another.)
Aside from that, I don't use a lot of the custom game options. I've found that the AI doesn't cope with those settings very well, with the exception of No Tech Brokering, as noted above. For example, Aggressive AI slows down the AI's tech rate considerably.