did you try to send a message to yourself? Maybe it appears that you are sending them but really not. When you do that go to your send messages, and there should be a check mark if it was sent and received to a vzw person ( i.e. yourself ). The green arrow says it was sent, but no delivery confirmation received, and finally a red X for failed message. You can also look at the detail by clicking options then message info as well. I would call tech support from a land-line phone and give them the results of your test to yourself. It could be a simple as texting being disabled, or a problem with the phone.
Also, as simple as it sounds, have you done a battery pull?
I'm having the same problem and I've tried taking the battery out and putting it back in, I've had friends send me text messages, I've sent them to myself from my phone and from my e-mail address...some of them I get just fine, some of them I get really late, some of them I don't get until I send the same person another text message, and some of them I don't get at all!