I play at King and have had several very peaceful civs. Here are some of the strategies I use:
1. Start position. If you start with a bunch of neighboring civs practically on top of you, then you're going to be at war before very long because you're all competing for the same land and same resources. Keep restarting until you've got some room to expand between you and the other civs. Also, shoot for a continent with 1-2 other civs, tops. Best of all is being alone on a small continent, however, you won't be able to trade other civs for luxuries to keep your happiness up until (most likely) you invent the caravel.
1A. You also want to look at WHO are your neighbors. For example, China or India will usually leave you alone (as long as you don't botch #2). Japan or Germany, you're going to get invaded at some point no matter what you do. Mongolia and the Aztecs will bluster a lot, but as long as you follow #2 and there are easier targets around, they probably will leave you alone (and by about the Renaissance, everyone will be going to war with them for being jerks, so they'll be too busy or too shattered to bother you after that). Attitudes of the other civs are very dependent on the situation - Rome, America, the Greeks, Siam, and Spain, for example, are voracious expansionists, but if it's easier to expand into unclaimed territory or at someone else's expense, they normally won't bother with you. England and Babylon seem to prefer middling-size empires, so if you're in their way, you may have trouble, but if you're far enough away, they'll probably be happy with what they have. And so forth.
1B. Look for choke points - mountain passes, narrow strips of land, etc. Plant cities on them as soon as you can and deny your neighbors Open Borders until you've filled up the land you want for your own empire. Strong fences make for good neighbors. If your neighbors start planting cities next to yours, it's going to be a lot harder to keep the peace as you each grab luxury or strategic resources the other considers rightfully his, etc.
2. Keep a strong military. Garrison your cities. Keep your units up-to-date. Build defensive structures like walls and castles. Yes, it's going to take away time & hammers from the things you'd rather be doing, but if you're weak, you're inviting the other civs to come steal your lunch money. Basically, you want it to always be easier for the bullies to go pick on somebody else.
3. Keep your word. If a neighbor gripes about you settling too close to his borders, don't apologize and then found a new city right next to him. They hate that just as much as you would.
4. Don't get sucked into other people's problems. You'll take a hit if you have a Declaration of Friendship with someone and then refuse to back them up in a war, but it's better than fighting a war you have nothing at stake in.
5. Except when it can't hurt you to declare war. Sometimes you'll be asked by an ally to declare war on a civ so far away you have no chance of ever actually doing any fighting - you'd be hard-pressed to send any units in time even if you wanted, which you don't, and they'll be too busy fending off invaders to bother with you. Consider going along to keep your closer neighbor - the one you really have to worry about - happy. Yes, you are technically at war, which isn't exactly peaceful, but you'll never do any fighting. There are some caveats, though -- if you declare war too many times, you'll get branded as a warmonger even if you never see combat. Also, be sure you don't have any vital trade agreements or research pacts with the would-be enemy OR ITS ALLIES. And, of course, be sure they don't have an ally close enough to actually cause problems for you.
6. Don't be warlike. Don't culture-bomb your neighbors, annex city-states, or raze other civs to the ground in vengeance if they do invade at some point, etc. Seems bizarre, but we've seen posts from people who gripe Civ V is broken because they are treated as warmongers after destroying "only" half the other civs.
7. Don't expect everyone to like you all the time. Other civs are going to be guarded, even hostile, at times. Some are going to denounce you. The other AIs want to win the game, too -- they aren't going to just sit back and smile mindlessly at you as you run off with the prize. It may not always seem "fair" to you - "I only culture-bombed your capital because you built a city next to a resource I wanted, so why are you mad at me?" - but the other civs aren't playing the game from your perspective. They're playing from their own perspectives.
Hope that helps. But, yes, it is possible to pursue a peaceful strategy.
Still, always expect to be attacked, the AI even with all it's faults, is trying to win. To expect them to let you walk all the way without trying to stop is crazy. You certianly would not let Rome walk all over you. 
