favorite civics can help so much! they can give you a big boost and they can really affect how the AIs feel about each other. you can manipulate that to your advantage when you want them to like each other less. yesterday's example:
i wanted hammurabi's land (he had wine but i didn't). pacal liked him, and i didn't want to earn a permanent -1 "you DoWd our friend" penalty. so before i declared, i used a spy to change hammurabi out of Hereditary Rule, which is pacal's favorite civic. instantly pacal quit giving hamm +6 credit for wise civics and dropped from pleased to cautious, perfect. i declared but didn't get a -1.
since i'd gone to the trouble of changing to despotism, i was a brat and used spies to change shaka and pacal to it too

their tech rate slowed way down for some reason. it was really easy for me because i had cristo redentor and was back to normal next turn, but they had to wait. obviously this doesn't work so well if you don't have CR, but it's something to have in your bag of tricks.
sometimes i give mansa a discount on economics, since FM is his favorite civic and i can't get credit for using it until he can use it too. gus almost always get constitution once i think i have statue of liberty safe if i'm not picking on him, since chances are i'll be running rep and he loves it too. if being friends with toku is
really important to me, i'll give him banking cheap and run merc.
one game i stayed in HR even after i captured the pyramids and wanted to change to rep, so that alex would stay at friendly. it was worth it, since together we got isabella out of the way. after that i had shrine cities, beautiful land and a great relationship with alex so i did feel safe changing to rep. his favorite civic has changed in BtS, but that's an example of just how much i pay attention to that stuff sometimes, and i'm convinced it helps me. then again, i'm far worse at the warmonger stuff than everybody else is, so i need every bit of help making sure the other folks don't pick on me until i'm ready! i need to pick the timing of wars, not the other way around, that's for sure.