Several people have been reporting Wi-Fi problems after updating to iOS 6 on both iPads and iPhones. The connection might work sometimes, but it usually cuts out or takes forever to connect to anything, only to time out shortly after.
It turns out this isn't so much a bug in iOS 6 itself, but rather in the update process from iOS 5. The network configuration gets corrupted during the update, causing connectivity issues.
Fortunately, there is an easy fix that won't require you to reset your entire phone (though it will require you to re-enter each of your Wi-Fi passwords).
Step 1: Reset Your... more