2-3 calls an hour is NOT normal and generally NOT the network. I had AT&T for 3+ years and dropped a total of 3-5 calls EVER over that period using an iPhone 3GS and an iPhone 4. Conversely, a buddy on Sprint drops roughly that many per week. I'm now on T-Mobile (just because its $80 cheaper a month than AT&T) and have dropped 2 calls in the first month I've had the service. Call AT&T and see what they can tell you. Exchange your phone. Check that your SIM card is making proper contact in the phone, etc.
Re-emphasis: It really does depend on where you are. Some areas, their service is fine. Where I live presently, not so much, which is ridiculous because I-70 West to ski country enters the mountains not three miles from where I live and work. In this particular case, it's a perfect storm of geography and dense user base, but they could and should fix it by deploying several infrastructure-grade microcells around the area. They evidently haven't, and the result is that you can be standing in my living room and watch the reception bars flicker between 0 and 4. Load an app to identify towers, and you discover the reason: the connection is doing a dance between three different towers. With that kind of handoff rate, coupled with high utilization, small wonder that calls get dropped.
To be fair, Verizon's service isn't quite perfect in this area for the same reasons, but it's generally superior to AT&T. T-Mobile seems better than both, for the two weeks or so that I've been using it. AT&T's problems largely started when they signed the exclusivity contract for the iPhone and didn't pre-upgrade their tower infrastructure to handle the massive volume of data traffic that would result, and they've been playing catchup ever since.