Sure. It's called a "bridge". Some routers will do bridging, and others won't. And then there is always a question of performance with encryption and/or different clients.
However, you might want to give consideration to an "
ethernet bridge". It will only do WPA1-AES, but you can slap a 12dB "Cantenna" on it, and get a huge range boost. There's also 18dB flat-panels about the size of a shoe-box in surface area. Getting a router that can take external antennas and slapping a Cantenna on there will also give you far greater range. You have to be careful about interoperability between brands, but I've paired up with lots of different AP's using that Buffalo client. Some routers put out more power than others, or can be re-flashed with a "hacked" firmware to put out more power.
Unless you know that you really do need a "bridge" AP (such as if you're going to be serving lots of people in your neighborhood), you're better off getting external antennas and a high power client (ethernet bridge).