At one point in time, bicycle rear wheels carried only a single sprocket, or sometimes two for racers; one for flatland riding and a larger sprocket for climbing. (It necessitated stopping the bike and turning the wheel around to engage the other sprocket). Regardless of one or two gears, these wheels were dish-less; spokes from both flanges approached the rim at the same angle, ensuring uniform tension for drive side and non-drive side spokes, just like a modern track bike. A dish-less single speed rear wheel is the strongest design, but not the most practical choice for daily use. Derailleur systems enable riders to go everywhere, but rear wheel strength is compromised because the drive side flange is pushed closer and closer to the wheel's center line to make room for the gears. Manufacturers have tried a number of remedies; DT Swiss moves the non-drive side flange inwards more than most to minimize the left side/right side difference in spoke tension; some manufacturers employ a radial spoke pattern on the driveside, which can free up a few precious millimeters of flange placement. For me, I reckon one of the best ways to mitigate this difference in tension is to move the spoke holes in the rim to one side. Enter the asymmetrical rim.
Here's a diagram of the Pacenti Forza, a fine example in aluminum:
Asymmetrical rims allow the wheel builder to build a stronger wheel because the design increases the low side spoke tension to the tune of 15 percent or more; given that spokes break more often from too little tension rather than too much, this is an improvement. The spokes on the low tension side are not so prone to loosening over time, either. Here's a handy diagram to illustrate the basic idea:
Now, just to be clear; are dished wheels sufficiently stiff? Yes, I reckon so. We've been riding around safely on dished rear wheels for eighty years or more; for good info on lateral wheel stiffness, go to Damon Rinard's Wheel Stiffness database, (http://sheldonbrown.com/rinard/wheel/data.htm). However, notice that all the wheels evaluated in Rinard's database use rim brakes and, like it or not, the bicycling world is tipping its hat to discs. Unlike rim brake wheels, disc brake wheels use the spokes to transmit braking power to the rim and tire. As a wheel builder with no formal education in physics or the like, I instinctively believe that a disc brake wheel will behave better in all situations (braking, steering, turning, impact absorption) if left and right side spokes are bracing the rim with (close to) equal tension. It's an idea that's striking a chord with a growing number of component engineers; guys who use empirical data to design stuff. If I'm proved wrong I'll buy everyone a steak dinner, but I predict an increasing number of asymmetrical rims available both in carbon and aluminum, for both road and off-road use.