My bike has an electric motor that attaches to the rear wheel by way of its own chain and gearing system (sorry, I'm not a geek -- I bought it this way.) As CrimsonEclipse mentioned, there are kits you can attach to bikes in one of three ways: like mine, or by replacing the front or rear wheel with a hub motor, or a friction type that attaches to the tire. All of these are considered pedal-assist -- you still pedal but the motor can add speed or help you up hills. The more you pedal, the more range you get out of your battery.

I ride 17.5 miles one way over very hilly terrain (hills from 6 to 15%) on my commute. I've never run out of battery but that's because I pedal all the time. My motor only takes me up to 16 mph so I don't use it for speed -- I can achieve that on my own, at least on the flats. But it does help me up the hills which makes the ride shorter and more fun.

I'm awaiting delivery of a new sprocket that will increase the torque, though it will take even more off the top speed. But I've occasionally experienced thermal cutouts of the motor and I think the bigger gear will lessen the strain on it. Also, I have to zigzag up the 15% hill -- maybe I'll be able to go straight up.

Here's a site with some information on electric bikes and kits: http://www.electric-bikes.com/