According to Apple only a "very small number of iPad users have experienced issues with Wi-Fi connectivity", and that a patch is on the way, yet I see articles all over the web that indicate the problem is much wider spread.
Sure enough, the iPad I brought home just yesterday was also having problems connecting to the same Wi-Fi network that my other devices and computers have connected to for months without problems.
Turn off wireless security
The only reliable, guaranteed fix for connecting my ipad to my Linksys home wireless network was to disable security.
At first I was able to get my ipad to connect to my Linksys WRT120N Wi-Fi router without problems, but not when I tried it again after the iPad had been on stand-by. It recognized the wireless network and would appear to connect, but then would lose the IP address within a few seconds (instead giving me a bogus address of 169.254.108.158).
You can check your ipad's network settings by tapping Settings -- Wi-Fi and then tapping the blue arrow next to the Network you're connecting to. You will typically see an IP address that starts with 192.168 instead of 169.254, and most of the other network fields should have values (Subnet Mask, Router, DNS, etc).
I tried several things that I've listed below, but the only thing that really worked was to turn off wireless security for my Linksys router. It's not as big of a risk as you might think, because my wireless router signal hardly even makes it out to the edge of my small backyard.