Ask some people about household projects (particularly the IKEA type) and they're likely to tell you that Allen keys are the bane of their existence. They look funny, they come in different sizes that are annoying to keep track of, and the typical bent wrench design lends itself to inefficient ergonomics compared to your bog-standard Phillips head screwdriver. Granted, for most household jobs (especially when simply trying to assemble pre-fabbed furniture) Allen keys aren't the best way to go. Being able to quickly screw something in overtakes any torque or fastening advantage. When it comes to more serious projects (like, say, rebuilding a 250cc motorcycle) Allen keys start to really come into their own. Let's brake it down:
Allen Keys Have a Terrific Torque Advantage
Specifically, a mechanical advantage. You remember that concept in high school physics right? In a dirty summation, it's a principle that allows tools, even simple lumps of metal like Allen keys, to multiply the effectiveness of the force exerted by the human body. In effect, the Allen key becomes a second-class lever, with the resistance force near the fulcrum (the screw). Second-class levers have a mechanical advantage grater than one, which makes them ideal for removing stubborn screws.
This isn't an ideal situation when you're putting together an entertainment center with low resistance, but it allows you to multiply your muscle power when screws get stuck when you're trying to remove your carburetor bowl.
Allen Keys Can Reach Anywhere
Another inherent advantage of the bent wrench design is that they can reach into extremely tight spaces without effecting how the mechanical advantage is applies. Try tightening or loosening a screw at an angle and see what I mean. Tight confines doesn't have a practical effect on Allen keys except for reducing the arc you have available for actual wrenching (and ramming your knuckles into cylinder cooling fins).
Allen Keys Are Strip-Resistant
The genesis of the Phillips head came from wanting a screwdriver that wouldn't end up stripping the screws. The pointed design of the Phillips head means that the screwdriver would automatically disengage when too much torque was applied. I've found that, in practice, this often meant stripping the screwdriver instead of the screw. Fun.
Allen heads, on the other hand, are usually deep enough and through distributing the torque through a wider surface contact area thanks to the hex design, become very strip-resistant. Excessive torque is transferred more thoroughly through the screw (as ideal) rather than in trying to bend and strip metal.
So what does this all mean? It means that hex heads are actually ideal for the type of heavy-duty fastening jobs typically found on bikes, cars and trucks.