same here with a first-day AT&T iPhone 4. At first I thought it was my MyFi, but I remembered my OTA updated iOS6 iPad 3 connected to Wifi no problem earlier in the day. My iPhone 4 is a thru-iTunes clean restore to iOS6. I did attempt the Reset Network Settings, Airplane mode, reboot, etc.
Looks like there always has to be at least one big issue per iOS release, lol.