Straight: Plain and simple, is simply more convenient reach-wise for some [one position]
Riser: Variations with sweep back and rise, more comfy riding position [one position]
Bullhorn/Aero: Awesome for climbing, nice to stretch out on, flats or horns are good (my old flop/chops are still my favorite) + you win at skidding
Track Drop: Assuming brakeless, wins the aesthetic contest for me, aero for racing, get down low - badass (not very practical for road riding)
Mustache/North Road: These and other touring variations have different bends, mustache has a bunch of hand positions - fun to try, not for everyone
Road Drops w/ Hoods: Hybrid of straights, bullhorns, and track drops with ergo advantage, there's a reason why they are the staple road bike cockpit.
Go nuts!