Wind turbines tend to look like windmills or giant propellers, and the design does in fact borrow from that. But that isn't the only design that's ever been tried.
At Sandia National Laboratories wind energy experts are looking at vertical axis wind turbines, (called VAWTs). VAWTs have a couple of advantages over traditional horizontal-axis designs, one of which is that the drive train mechanism is close to the ground and thus easier to maintain. They also aren't as complicated and have a lower center of gravity. If a VAWT system could be made to work, then it might make wind power cheaper.
VAWTs are also simpler in one respect: they need not face the wind, since the wind will turn them from any direction. That means there are fewer moving parts and less maintenance - an important consideration when building an offshore wind farm.
So why aren't they used more often? VAWT designs generate different loads on their drive trains. That is, a traditional wind turbine has blades that face the wind at a certain angle. The angle of those blades can be changed to account for different wind speeds, which keeps them moving at a relatively constant rate, reducing the wear and tear on the drive mechanism.