It's always "fun" to experience an issue just before a fix for it appears in our TUAW newsroom. In this case, I was receiving iMessages from my wife, but she wasn't seeing mine. Fearing that the worst had happened and I had been run over by a truck (while sitting at my desk), she called me. It turns out that a lot of people are running into this Messages app bug with iOS 7, where iMessages aren't being reliably sent out.
Fortunately, there's a quick and easy fix for this issue -- just restart your iPhone or other iOS device. In case you're new to the iPhone/iPad world and don't know how to shut down and then power up your device, it's easy.
Just push down