You can turn your Wi-Fi router into a repeater, but if your router doesn't have the firmware or your walls aren't wireless-friendly, you can get similar results with the addition of some powerline adaptors and settings tweaks.
Photo by Andy Butkaj.
Downloading new firmware has a few downsides, most notably the fact that it's a pain to install. Furthermore, you may not be comfortable installing third-party firmware that hacks your device, if your router doesn't have the required firmware available. Technology blog Tested has created a guide to expanding your Wi-Fi network using an old router and a device called a powerline adaptor instead.
Essentially, instead of wirelessly "extending" your network, you'll be turning your old router into an access point and putting it in the dead zone of your house. It'll still need to be connected to the network, though, which is where the powerline adaptors come in. Powerline adaptors plug into your A/C outlets and connect to your network through the electrical wires already installed in your home, and you don't need any kind of electrical experience to get them working. You could, of course wire it up via Ethernet, but you probably don't want Ethernet cables running all through your house - so powerline adaptors are a pretty awesome way to go.
You'll need to tweak quite a few settings on your router too, and the powerline extenders aren't super cheap — you could probably pick a few up for the same price of a regular wireless network extender — but if you have a house that isn't wireless extender-friendly (due to thick walls or a strangely shaped house), this is a great way to get wireless everywhere you need it. Hit the link for the full guide, and let us know your experience with powerline extenders in the comments.