Ok I tried searching for this but don't find anything that applies so here goes...
Playing Isabella/Spain, pretty low level. Trying for the first time to go for cultural, so kept only 3 cities (even though I cornered off half the pangea)
Anohoo, friendly with everyone, then suddenly India America and Iroquois all declared war on me. Then in the history it says they "backstabbed" me.
What does that mean exactly? Is the AI smart enough to trick me into being friends then attack me together!?
There's an actual modifier for the AI called "loyalty". It has a bit of randomness to it, as in America might have a modifier of "5 plus or minus 2". The lower the number, the more likely they backstab friends if it means getting what they want. Some civs have a near 0 chance, and others have a much higher. You should take note of who backstabs you so you know if you can expect it in the future. Note that "not being their friend" doesn't lower the chances they'll attack you, all that loyalty seems to mean is they take your friendship less into account in seeing if you're a good target.
I find the best way to stop backstabbing from neighbors is to get into a Friendship with them, and find a common enemy to hate. Give them a different goal and then they won't go after you.
Don't sign Declarations of Friendship with anyone, ever. They allow the AI to ask you for stuff. All your stuff sometimes.
If you say No, you get a Diplo hit.
If, on the other hand, you say Yes, you get nothing positive whatsoever.
Yet you can't ask them for the same things --- and hurt their Diplo if they say No.
And if you are Friends with anyone, someone else invariably hates them and denounces you.
If your Friend ever denounces you, you take a worldwide Diplo hit.
Nothing positive whatsoever comes from them, only increasingly negative things. This may sound like I'm just bashing something, but this is really how it works. Stupid mechanic that can only hurt you. Never be anyone's Friend. You'll wind up accruing slightly fewer negative Diplo modifiers that way.
That's complete BS. I get gifts from DoWs, have proactively declared joint wars with DoWs, and have leveraged DoWs to get more "friendly" status with other civs all the time.
Of course there's negative things caused by a number of reasons that only happen in a DoW state (not helping out, not giving gifts, being friends with their enemies). You only usually see a denouncement if you're a complete ass to your friend. But if this didn't happen, they might as well label it "permanent alliance". The Declaration system is one of the few really dynamic things in Civ5 that makes sense past the initial 10-20 turns.
Without Declarations, we'd be back in the old days where the strongest civ declared war on their neighbor, and so on, and so on, and global politics wasn't affected by global politics. Now we see 3 on 3 civ alliance wars and other cool things happening. I've had a number of world wars break out which is something I've barely seen in previous civs or even pre-patch.
I'd say the global diplomacy is near the top of my small list that Civ5 has done right. It shouldn't be changed, it should just be tweaked.