I would say that "ride" implies (though does not dictate) passivity, in the sense that if you're riding in a car, someone else is driving. (Which is pretty much always the case with a train.)

A notable counterexample is in Chuck Berry's "No Particular Place to Go": "riding along in my automobile". (Then again his "baby" was "beside [him] at the wheel", so maybe she was driving.)

But, yes, it is common usage. Generally it implies that you were a passenger, unless you refer to the car self-possessively. "I rode here in a car" or "I rode here in Bob's car" both imply that you were a passenger, though the latter is somewhat awkward. (You'd be more likely to say "Bob drove me here" unless someone else was driving his car.) "I rode here in my car" implies that you probably drove.