Electric bikes use a small electric motor driven by a rechargeable battery pack to help you along. They are good for hills, carrying lots of luggage, or making sure you don’t arrive at work all hot and sweaty. The motors are not designed to replace your pedalling, just to assist it. There is a huge range available, but they generally fall into two categories:
Electric bikes are still bicycles, so have no road tax, no insurance, no MOT, no license plates, etc. To comply with this, they have to be limited to a maximum speed under power of 15mph (although you can pedal faster than this if you want, of course) and an average power of 200W (250W for an electric tricycle). At present in the UK, both E-bikes and Pedelecs are covered by this, although there are moves to make E-bikes conform to the same regulations as mopeds.
An Update on the legal issues (Thanks given to Ben @ Kinetics)
UK Electric Bike Law
The current situation: At present, all electric bicycles sold in the UK should comply with the EAPC (Electrically Assisted Pedal Cycle) Regulations. These say that an electric bicycle is classed as a bicycle if the motor will not provide any power above 15mph, and that the motor must have a continuous output of no more than 200W. All cycles which fall within these limits are legally treated as bicycles - you can ride them without a license, and they don't need insurance, road tax or a helmet. Any cycles which exceed these limits are classed as mopeds, and must be type-certified, insured, taxed, etc.
What is coming: The EU wants to standardise the type certification legislation across the whole of the community. For this, they have issued a Directive (2002/24/EC), which states that any electric cycle which conforms to certain restrictions will be exempt from type certification, and will be treated as a bicycle. The new restrictions are: maximum of 25km/h under power (approx. 16mph), maximum continuous output of 250W, and the cycle must stop if the rider stops pedalling.
So what does this mean? Basically, the new restrictions will allow electric bikes to be a bit faster and a bit more powerful, but you will have to keep the pedals turning to keep the power on, which is not currently required in the UK.
When does this happen? The Directive comes into effect on 9th May 2003 - EU member countries then have 6 months to put the legislation in place.
Who will this affect? Many manufacturers already build their bikes to German standards (which are identical to the new directive), so they will not have to change anything. Other manufacturers should modify their designs before May 2003. A very important point is that the legislation will only apply to the manufacture of new bikes - if you buy an EAPC-legal bike before May 2003, it will still be fully road legal after May 2003 - you will not need to modify or upgrade your bike.
There is a lot more info at http://www.extraenergy.org
There are three ways that the motor can drive the bike - by rubbing a roller on the tyre, driving the chain (like you do when you pedal) or driving one wheel directly from the hub (as shown in the picture above). The first method works quite well in dry, dusty climates, but in the UK is not very effective. The second method is good, but you can sometimes find that you need to pedal in a gear which is good for the motor, not for you. The third method is generally the best.
Electric bikes are heavier than other bikes. You have to carry around the extra weight of the batteries (basically a lump of lead, in the case of Lead-Acid ones), so the bike can be hard to pedal without assistance, and to carry up stairs, for instance. The lightest electric bikes are currently around 20kgs, with 17-18kg ones in the pipeline - cheaper electric bikes can be 10kg heavier, or even more.