Au contraire - getting the AI to like you can pay big benefits. If you are bigger than them they will pay tribute; if you are smaller you can ask for gifts. Many players do the One City Challenge this way.
The key to making the AI happy is giving gifts and not backstabbing, even another AI civ. Once you betray one the rest are wary of you. The best thing to gift is tech that is a little behind what you working on. Be careful about gifting military techs to Militaristic civs, although it will make them more happy than a civilized tech (like Ceremonial Burial or Currency). As soon as you get Republic give it to everyone; some civs will switch and be more peaceful (one way to pacify the Mongols!). Check the Foreign Advisor screen as often as possible and gather several techs to gift; if you can get them to Worshipful they willl definitely exchange maps with you, sometimes at lower attitude levels too.