I had a similar issue with my Samsung Captivate on AT&T. It started Monday night 7/23 at midnight. I could send texts, but not receive them. Everything else was working fine, calls, email alerts, browser, etc. I had not downloaded anything new to the phone, it just stopped receiving texts. I spent an hour on the phone with tech support and they checked the account for any blocks, reset me on the network, had me turn off my phone and they sent something to reset it. None of this worked. The next step was for me to take the phone to a store.
I took it to an AT&T store the next day and they tried putting a new SIM card in the phone, but no luck. The rep said that I was eligible to upgrade the phone, but I said that I didn't want to do that because I was not convinced it was the phone causing the issue. After several of the reps at the store worked on it for a while, one rep had the answer.
Here is what he did that fixed it. He put MY SIM card in another phone in the store (some cheap free flip phone) and then sent a text from that phone to MY PHONE NUMBER. When he did that, all of my backed up text messages came flooding onto this flip phone. We put my SIM card back in my phone and everything is working fine. I had to go thru the texts left on the cheap flip phone and forward the important ones to my phone so I had them and then clean them off the flip phone. He said that he doesn't know why this fixes it and they see the problem so rarely that not many reps know this trick.
Take your phone to a store and try this trick to see if it works. Beats doing a factory reset on the phone which wipes out all of your pics and apps.
Hope this helps. Good luck.