Can a wireless router be used as a range extender?
Solution 1:
I've used a dedicated hardware repeater before and ultimately replaced it with a hardwire run. The speeds I was getting on the WLAN were pretty crappy when I was running through the repeater, and with broadband speeds now creeping up to the levels where it can saturate a 802.11g network that's a significant thing now. Add in some remote TV viewing from my MythTV and it just wasn't holding up.
I bit the bullet and surface-mounted a Cat-5 cable to a spot in the middle of the house and put my access-point there instead. It improved reception in the places we needed it and speeds were noticeably better.
Another option to look into if a hardwire isn't in the cards would be to see if your AP has replaceable antenna. That can save you from potential spousal-veto regarding an ugly wire snaking across the house. Upgraded antennas can extend the range enough to pick up those dead spots.
Solution 2:
Generally speaking, it is. You need to provide more specific information about the model of router and the firmware it is running, however.
I would looking into the DD-WRT firmware if your router supports it. It will allow you to use your router in this mode and it will add many additional features.
Solution 3:
While some wireless routers (and access points) can also function as a repeater, you need to take into account for every repeater you add to the "chain" you effectivly halve the speed/bandwidth.
A better way to acheive greater wireless coverage would be to run cable, and have an access point instead of a repeater. Give both the wireless router and the access point the same SSID and encryption/key and your wireless devices will be able to move between to two seamlessly.
Solution 4:
As others have mentioned, most consumer-grade routers do not have Wireless Repeater capability in their firmware. If you have a router supported by one of the Open Source firmwares (such as DD-WRT, OpenWRT, or Tomato), then you may be able use them instead. DD-WRT maintains a database of hardware it supports on its website, although the original router most of this work stems from is the venerable Linksys WRT54G (prior to hardware rev-4).
Once you have the firmware flashed, it is relatively easy to get it into Repeater Bridge mode. Here is a HOW-TO from the DD-WRT wiki.
I have pretty much this exact setup configured at home with a pair of WRT54GL routers (~$50 each at pretty much any place that sells commodity hardware, both computer stores like Tiger Direct as well as places like Best Buy). The only thing to watch for is a little extra latency if you're on the repeater and sometimes the two can briefly lose sync. It works just fine with WPA security on both routers. I'd also suggest using a different SSID for the Repeater so you can easily keep track of which your devices are connecting to (as opposed to letting the device firmware roam between them... sometimes you get stuck on the far router which results in a pretty choppy signal until it decides to roam back)