I actually have an electric bike. Used it in my old neighborhood where we had some horrendous hills and lots of them. Gave it to my dad when I moved to the flatlands.
Mine is a currie USPD equipped folding full sized mountain bike (frame folds in half and the wheels and seat come off) so it can be carried in a trunk. I bought it on ebay for about $350. The USPD kit can be added - by a bike mechanic or someone with extensive knowledge of bikes - to an existing bike, and there are several premade bikes using this add-on kit.
What you'll find in these are three types. An "add-on" with friction wheels that engage the front or rear wheel (like the ZAP bike), an "add-on" with an extra gear set on the left side of the front or rear wheel, and an "assist" bike that doesnt have its own separate gear setup, it just boosts you when you pedal. The first two can propel the bike on its own, the latter only provides so much help when you pedal first.
Some of these bikes are VERY small, and some are VERY heavy and all have weight restrictions. Mine was a full size bike that weighed about 40lbs on its own, with a load limit of 200lbs. I weigh 215, and it was too much for it, so the weight limits are not conservative. The weight isnt hard to figure out...these things carry 24 and 36v battery packs usually made up of 12v small lead acid batteries like you might find in a home battery backup unit for a PC. Some bikes are using Nicd or Liion batteries, for twice the price. The speed and range are usually also a little liberal, presuming the passenger is a gerbil and the road is downhill all the way, both ways.
Some of the add-on kits have motor overheat problems. Mine did, so I added a big AMD CPU heat sink to the motor "can". Worked like a charm, but looked pretty funky.
For a non-add-on look for those with a few buckaroos, Heinzmann makes some very elegant and well made bikes. Mercedes even made a beauty once. Ford and Lee Iaccocca got into and out of the business pretty quick. Giant makes a well regarded bike in this area, with a very strong motor. You can get these on ebay and on "fell off a truck" sales for $500-600, but they usually get 750-1250. I actually considered upgrading to a Heinzmann and won one on ebay for $650 and the seller weaseled out on selling it to me.
Laws around these are funny. Many states consider these with a motor up to a certain wattage to be nothing more than a bike. Some require helmets, drivers licenses, and so forth. Some consider them to be mopeds. Many recommend that you carry a moped type insurance policy as an electric moving at 25mph with a set of acid batteries strapped to it can do a little more damage than a regular bike.
Kind of a fund tinkering experience, and I can see where an ER'ed engineer could have some fun with one of these for a week or two, but I wouldnt want to rely on it for any sort of transportation.