Interesting question; many civs have their dark sides. Greece and Carthage have those showstopping early defenders. Rome and Germany are very triggerhappy and make dangerous neighbours at the start of the game. Rome and Japan have those annoying "balanced" UUs which offer little advantage in human hands, but let the AI off the hook of its own tactical incompetence. China, Arabia, Spain and Scandinavia all have dangerously mobile UUs, which though rarely used effectively are still a threat. The Mayans have a lot going for them (traits, slave-taking, an ATT/DEF balanced UU) and if the Mayans get a continent to themselves, they can make pretty tough opponents.
But my final vote goes to Rome. If Julius starts nearby, there is a danger of an early archer attack, and if he starts far away there is a danger that he will procure iron before there is time to go over and beat him up. And having a bunch of unkillable swords plodding inexorably across your empire is never fun.