CAN LEAVE A TRAIL. So does your smart phone. According to Farhad Manjoo at SLATE, in his article "Fear Your Smartphone", "It’s totally rational to worry that your phone is tracking everything you do."
Trevor Eckhart, a 25-year-old software-systems administrator in Connecticut, posted internal documents and a scary video showing what our phones know about us. Eckhart exposed the capabilities of Carrier IQ, a company that makes software used by several carriers and phone companies to gain “insight into their customers’ mobile experience,” as the firm describes it. Carrier IQ’s software, which is completely hidden from users (and could continue to work even if you opt out of your phone’s diagnostic monitoring), is capable of logging and reporting back pretty much everything that happens on your phone. It can see the apps you use, the sites you visit, your physical location, and it can even log your individual keystrokes, which means that it can read your text messages and passwords.
Apparently, unlike other phone makers, RIM's products don't ship with it, but service providers can install it. Then there's Echelon and Communications Security Establishment Canada, who may be listening in. Seems like the anonymous, pay-as-you-go cheapo phones may not disappear anytime soon, especially for border crossing.