So I'm constantly reading people complaining about how it's impossible to have diplomatic relations with the computer in Civ V. I'm here to tell you you're wrong. It's not impossible to live peacefully with your neighbors, you just can't do it the way you did in Civ IV. In my second game on Prince difficulty I won a cultural victory and only got into two short wars of my choosing. Not once was I attacked, but the key was that I ALWAYS had enough military to effectively defend myself.
Here's the first thing you have to realize about Civ V. The AI leaders now simulate another player, not an AI ruler. They play to win. Granted, they play poorly, but they play to win.
In Civ IV the AI leaders were simulations of another government. If you got your relation up to a high enough positive number, they wouldn't attack you cause hey, you're friends. Now the AI leaders just want to win. If you want to build to a cultural or diplomatic victory, you still need a military strong enough to convince the AI you're not worth attacking, because attacking counters every other strategy to win the game. It doesn't matter how high your culture, technology, or diplomatic relations are if you can't effectively protect your cities, and the AI adheres to this philosophy (admittedly too much imo). Imagine what a human player would do if he saw you had no military and five wonders =p
Now for my own personal experiences. In my last game, my immediate neighbors were Rameses, Catherine, Suleiman, and Napoleon. My wars were against Rameses to take his capital on my border and its wonders, and Suleiman to save a cultural city state. I didn't take any of Suleiman's cities, just pillaged hundreds of gold from his tiles.
I formed early Pacts of Secrecy against Rameses and Suleiman, because Catherine didn't like them. Other than that, I refused mostly any pact of secrecy against the other 5 rulers and was constantly in pacts of cooperation with them. I occasionally donated excess luxury resources to my neighbors when they asked, was constantly making 1 for 1 luxury resource trade agreements with all the other civs, and was constantly in research agreements with the other nations.
A few highlights regarding Catherine in particular. Part of my strategy was to keep a monopoly on gems and wine to trade to other rulers to keep my relations up. There was one good settlement spot left with access to two wine, and I was about to settle it when I saw Catherine had moved a settler into the exact spot I wanted. I asked her not to settle new cities near me, and she actually agreed and withdrew her settler. The next time I spoke to her she was still smiling. A few turns later I saw her martialing an army at my borders, and thought I was about to meet the famous bipolar AI. But no, she just asked for open borders and went to war against Napoleon, along with the rest of the world. It's worth noting Napoleon had just conquered Rome completely.
Now I'm not saying diplomacy doesn't need some work, because it certainly does. I think the biggest problem is that AI players over-react to conquering other nations' cities. However, I believe the problem most people are having is that they're trying to work the system the way they did in Civ IV, and that's just not how it works anymore. Now maybe circumstances were just right in my game, but it still proves that it is possible to play peacefully.
I'd love to hear if anyone else has played games this peaceful, and would be happy to answer any questions about my game in particular.
tl;dr: Diplomacy works, but you have to have the military to back it up. The AI plays to win now, not to simulate.