As reported by a few places (and acknowledged by apple), evidently a "small percentage" of imessage users have had difficulties since applying the iOS 7 update (myself included). Symptoms are that users can receive messages, but sending just never goes through - never changes to a text message either, so it's all kinds of hosed up.
iOS 7.0.3 is apparently already in the works and will resolve the issue. In the meantime, if you see your imessages just pausing and never going through, restart the phone - seems to correct the situation, at least temporarily.
Anybody else seeing this problem?
Source: ABC News - iOS 7 sucks