Apple has released an update to iOS 6.1, hopefully fixing the connectivity problems that have stopped users from sending text messages or going online. Version 6.1.1 has showed up for us as an OTA update; its change log indicates it "fixes an issue that could impact cellular performance and reliability for iPhone 4S." iOS 6.1, released in late January, added wider LTE compatibility for some devices and improved features like Siri and iTunes Match, but it caused intermittent network connection problems, leading European carrier Vodafone and other companies to suggest people hold off on downloading it. Assuming this has indeed resolved the issue, these warnings can now be safely put aside.
Update: Vodafone says that iOS 6.1.1 has fixed the iPhone 4S connectivity issues, and is advising customers to update.