When a user gets a notice of new voicemail on a Cingular Blackberry, where is that stored to keep track of the number of new voicemails for the icon on the front screen? Is it in the SIM chip or in the Blackberry's memory?

This information comes to the handheld as part of the VM transaction--the network is telling your device how many VMs are present.

But the number of new messages has to be stored on the device somehow. That's my question. If I turn off the antenna, turn off the Blackberry and turn it back on, the number of messages comes back, with the antenna off, so it's not getting it from the network unless I'm missing something.

It's stored on the phone.

Ok, so it is stored in the Blackberry memory? I had seen some references at least from T-Mobile that incoming text messages were stored on the SIM card, and since voicemail notifications were basically sent as text messages, I thought it might be stored on the SIM card.

Yes, it's stored in the blackberry memory.