They'll denounce you if
1) You denounce them
2) You are competing for something, usually CS, land, wonders and their flavours are strongly aligned to one of those.
ie: Rameses once denounced me because I built too many wonders. That is very extreme however. Most civs are not like him. You might see 'covet wonders' penalty in the diplo screen, but many will remain your friends.
3) You break a promise
4) Your friends denounce you
5) Their friends denounce you
6) They see you as a threat (score competition/common borders) - this becomes the big driving force as the game nears the end. AI civs near your score or share a common border who aren't friendly will very likely be plotting against someone and you might be one of their targets.
It's actually fairly easy to keep DoF chains going, but you can't keep it going forever as things start to get messy with more than 2 civs in the mix and as many have shown, Diety play is all about manipulating DoF, bribing Civs who are already predisposed to go to war to in fact go to war, and watch them denounce.
The easiest way outside of bribing is to follow denouncements of your neighbours closely in the early game. If you see a Civ denounce someone you deem to be a threat (ie: Strong AI civ that will cause you problems later); Denounce the Civ too. Instant power block. I've carried multiple early game relationships like that all the way to the end.
Geography is also important. It's best not to share borders with a friend in the ealry game or their expansion instincts will clash with yours and they could end up backstabbing you to grab a border town.
That said, if you play fairly, don't break promises and don't DoF everyone making you look flakey, Creating blocks is super easy in Civ5 simply following basic rules of friendship. But the game does also have inflection points. It starts off fairly easy. Most every wants to be friends. DoF chains are very easy to make and maintain early.
The first inflection is around turn 100 when AI core is set and they are pushing for ring 2 expansion. Early friends may not like each other any more, so you'll have to adjust.
After renaissance, it becomes hard to keep DoF chains of more than a few Civs, because the Civs in your block will often not like each other, and if you DoF them all, you'll get hit with the 'you friended my enemy penalty' This is when you really pare down your block to 1-2 Civs that aren't tangled in hatreds.
That doesn't mean you can't have big DoF chains in the late game, but a realignment is necessary. You'll probably keep 1-2 of your best friends, plus pick up several new Civs who don't hate your friends. You'll have to ditch Civs who will cause you trouble.
That said, I've run power blocks where I have in my mix 1 or 2 civs who hate each other. I do get hit with the 'friended my enemy' penalty, but because I only did it to one Civ both ways, it's not a diplo breaking penalty and the Green items on my list far outweigh the red ones and only 2 of the civs are affected.
I really need to finish that article in the academy.
kaspergm said:
furthermore UI has a huge flaw that when someone asks you to form a DoF, you can't see what their relationship is with other factions (something that will hopefully be fixed), which is something they will hopefully fix (or someone can mod in).
I do not agree with your assment of the diplo system, and none of the things you've said are true flaws, aside from being different from what you're probably used to in previous Civ games, but this item is indeed a flaw.
InfoAddict (mod) does let you check relations before you agree to accept. I had a lot of trouble for a long time, because someone would call me up and I would have no clue if I can friend them on that. However, as I played more games and grew more confortable with the diplo system, especially post G&K when diplomacy is significantly more stable I've actually learned to just pay attention to the notifications and not click through 'next turn' like a madman. I've pretty much mapped the relationships in my head as I play. It's actually a lot of fun that way. It's more personal than having to refer to a chart every time you do diplomacy.
Though I feel not everyone can or is willing to do that. I'm personally quite satisfied with my own solution
If you really need it, get InfoAddict. It also gives you lots of graphs and tools not in the base game. Some consider it a cheat because you know so much information, including the exact relative military strength of each Civ. My advice for you though is to just play more games and pay more attention to the notifications and to global politics. Civ5 does away with a lot of microing on the economic level, but it does expect you to micro diplomacy by paying attention. I think that's the paradigm shift a lot of people who don't get Civ5 hasn't learned yet.