In addition to the AirPort Extreme, Apple has the AirPort Express in their line of network products. The previous version you still had to plug into the wall, but the new model resembles Apple TV in terms of design. Hardware.Info tested it to find out how well it works.
If you need to expand your wireless network at home, then adding an access point is a good solution. It will increase the range without impact the bandwidth. If you instead used a repeater to expand the wireless network completely wirelessly, you would lose bandwidth. If you want to install an access point on another floor, you do need to run a cable from your router to the location where you want your access point to be. If that doesn't pose a problem, then this solution is preferable over using a repeater. The signal from a router to the access point is generally more stable since it goes via a cable, and you don't lose the bandwidth like on a repeater due to the simultaneous sending and receiving of the wireless module.
The Apple AirPort Express is not limited to functioning as an access point, it's also works like a router. However, the likelihood that it will be used in such a manner is small, since it has only two network ports - one for the WAN and one for the LAN. It is one more than the previous version had.
It's of course possible to increase the number of ports by adding a switch, but then it would make more sense to buy an actual router. If you combine the purchase price of the AirPort Express (£81) and a switch, you can almost afford a high-end router.