There have been a few reports of AT&T customers not receiving text messages, but it's unclear if this is widespread or not. Some users have reported that they are only affected when texting certain people, while others say they can't receive texts from anyone. There doesn't seem to be a clear pattern yet.
AT&T has acknowledged the issue and is investigating, but hasn't released any further information. In the meantime, affected users can try restarting their phones or sending texts as iMessages instead (if both parties have iPhones). We'll update this post as we learn more.