In fact, any phone is connected in a way that your position can be learned.
Traditional phones are always in one location, and cell phones can have their
location detected by triangulation.
Actually, it's not a bad thing that your position can be detected,
necessarily. It's good in particular that the location of calls to emergency
telephone numbers; someone could be unable to speak and alone, for example.
The real problem is that the software in the phones is proprietary, so you
the user are unable to be sure that the phone is not communicating with
towers or using its GPS without turning the phone completely off (and since
computers are never truly off, and some phones might not even be in the
regular pseudo-"off" state, that means taking out all of the batteries).
An ideal free OS for a cellular phone that doesn't have hardware that depends
on nonfree software or that is malicious would have a good set of options for
when the phone communicates with towers. I don't think any cellular phone
today has such options. It should be a standard option to simply shut down
all communications with cell phone towers during periods when you're not
intending to use the phone for communication. Instead, all we have is "silent
mode", where the phone still communicates with the tower, but doesn't notify
you of calls and messages. "Silent mode" sure has a place, but shutting down
communication with towers would work just as well in many cases where it's
used and prevent gratuitous tracking of people who aren't even using their
phones at the time.