IP Address Question? Security?

May be a silly question, just not well versed in these things...

If someone has your IP address (captured in email or by visiting their website)...let's assume someone computer savy (IT type), what can they find out about that address? I'm talking about the BB / RIM IP addy.

Any paid services where they could find your browsing history, that type of thing?

I've got a personal BB that doesn't change IP's with a battery pull, even though my work BB does. Strange. I just like to do battery pulls and change IP's every so often, but it doesn't seem to work on my personal phone (different carrier).

Nothing. BlackBerries don't use Static IPs. Your IP is randomly assigned from a pool of available IPs are required. Your personal BB should do the same..?
Regardless, it's not in any way "registered" to you personally, so even if someone did track your web activities, all they'd be able to find out is that SOME BlackBerry is doing whatever it is that you do, not you specifically.