Had the same issue 3 days ago following a settings reset and resync (Data not showing in Settings\About). I was on home wifi at the time. The About section found no number listed or carrier information with Data switched on.
A check through my Settings found that Location Services, though on, had turned off the Cell Network search Option. Once back on, I turned off using the hold button in slide red slider method, switched on again and everything was fine.
As a footnote, I have seen some solutions to other problems being given to reboot by this method but to then press and hold the Home button until the screen flicks to the home screen before bringing the Apple logo up. tried this to solve something else and found that this method works to track last settings saved. So if you make changes without resyncing and then reboot with this method, the changes are discarded for a last saved state. Just something to keep in mind if rebooting. Total switch off, wait, switch on and resynch with your connection active seems to be the way to commit the settings. This has worked for me. I am in the uk and have not experienced anymore problems for the last 3 days. I am on 3 netwrork, and Virgin Media Home broadband via a Linksys WRT54GS (EU-LA) model. 2.4Ghz 802.11g with built in speedbooster. Ipad2
Another thing I sometimes notice is that if i do not turn cellular off in Settings the 3g icon stays active on the top bar instead of indicating my home wireless,. However with iTunes open on my PC the device shows up and syncs normally, and any downloads i make to the iad sends my modem lights racing, so i know it is using home wifi.
One other thing I do do though is to keep Data Roaing switched off, as I dont need it. I left it on once and it used to drop my 3g regurlarly as it tried to lock onto signals from other masts. Since I have kept it off I have had no further problems when out and about.