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 on the power button on top of your iPhone or iPad for about five seconds. A red stripe appears across the display saying "slide to power off." Swipe to the right on that stripe to shut down your device. Make sure that the screen goes completely black (no spinning "rotor"), and then press the power button again for about a second to turn the device back on.
Now you should see all iMessages that weren't successfully sent, and should also be able to send new ones to your BFF.