UPDATE: New information from Apple's question and answer page contradicts the below statement from Apple's PR department, indicating that a data plan is required for iPhone usage.-----
Earlier today we reported on Apple and AT&T's announcement of rate plans specifically for the iPhone, all of which include unlimited data transfer. One interesting point in the rate plan press release missed by most, however, is the following:
"iPhone customers can choose from any of AT&T's standard service plans.
So apparently, the iPhone can be used without one of the provided data plans. This makes sense from a pricing perspective: for instance, an iPhone data plan for existing customers carries a base price of $20. A standard AT&T 450-minute voice plan with no data is priced at $40. The iPhone's least expensive plan with data includes 450 minutes and is priced at $60.
However, it appears that there will be no Visual Voicemail if a data plan is not included, only regular voicemail.
What is not clear is whether or not users will be able to access the Internet using WiFi with only a voice plan -- we would assume so.