I haven't had any problem free car, but I consider my current car (Mazdaspeed 6) reliable in that I wouldn't have a problem leaving RIGHT NOW for a cross-country road trip. The problems (so far) have not been show stoppers. I couldn't say the same about my previous car, a Contour SVT.
My wife has had vehicles that were pretty much problem free. She had a 1993 Toyota pickup truck. It was a stripped down model, with crank windows, no A/C, 4-cylinder engine, etc. It only had normal wear-tear (tires, battery), accident (hit a deer), maintenance and theft (three meth addicts broke side window to steal stuff, were eventually caught and most of the stuff recovered) happen to it. Her more recent 2005 Mazda 3s was also problem free outside of routine maintenance and limited life stuff like tires and battery.