If you've ever picked up your iPhone, seen 4 or 5 bars, then tried to go on the web or check mail only to get the popup "Can't connect to cellular data network" you've been bitten by this bug.
Sometimes the cell network really is down but sometimes it isn't and that's what makes this such a frustrating issue to trouble shoot. Details after the break.
Data and voice are separate services on your iPhone so you might easily be able to make phone calls and send/receive SMS but when it comes to using anything like Safari, Mail, or apps that need the internet -- you're dead. (And seeing those full bars and being dead is especially frustrating, like when you're Wi-Fi router is working but your internet connection is down!)
This one is easy!
Here's how you can try and fix it, least painful methods first:
If you're sure it's not your carrier:
Also frustrating is that this problem can be temporary -- carrier outage, too many people on the tower, error on your iPhone -- and it can fix itself on its own after a little while. It can also be a problem on your iPhone that doesn't fix itself and drives you crazy. Those are the fixes we've tried, if you're experiencing the problem let us know, and let us know what fixes have worked for you!