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.
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.
To turn off wireless security, you'll need to log into the administration web page for your wireless access point (http://192.168.1.1 for my Linksys from a computer that's connected to the router). Once logged into your Linksys, click "Wireless" and then "Wireless Security" and choose "Disabled" as the security mode. Be sure to save that screen before moving on.
If you're worried about security being disabled, you can turn off SSID broadcasting by clicking "Wireless" -- "Basic Wireless Settings" and setting "SSID Broadcast" to "Disabled". Your neighbors won't even see that the network exists. You'll have to tell your ipad what your network name is, but once it's entered it will remember it.
Here are the other things I tried:
Change the Linksys wireless router's network speed to B/G mixed instead of the default wireless-n, and the Channel Width setting to 20Mhz instead of the default 40Mhz.
According to this article on Apple's support site, ipad does not support 40Mhz. Scaling it back to 20Mhz didn't affect performance and fixed the connectivity issues I was experiencing.
One thing I noticed is that with wireless security turned on (using WPA2 Personal) it takes the ipad a little longer to re-connect to my Linksys wireless access point than my iphone and Macbook. Sometimes up to 60 seconds longer, so be patient and don't give up until you've waited about a minute for your ipad to reconnect after turning it on from standby. With security turned off, the connection time is instant.
My ipad also won't connect to wifi until I open Safari (again, when I have security enabled - connection time is almost instant with security disabled). That seems to be the thing that triggers the ipad to try to connect, and about a minute after opening Safari it successfully connects and holds onto that connection for a while. Sometimes it drops the connection though, so again I recommend just turning off wireless security until Apple figures out a fix.
Here are a few other tips and tricks for solving ipad Wi-Fi connection problems, taken from another page on Apple's support site: