As the OP who posed the question, I think I probably agree with the general consensus that it is usually a bad idea. But in the two situations I experienced, I was drawn to offer the rides and it was the right thing to do. The first woman was a little down on her luck and might have been a bit mentally unstable, but I talked with her for several minutes before she asked if I could give her a ride. I was close to telling her no, but something drew me to say okay and she was very thankful for it. I admit it was probably a bad decision that I might not make again, but it all worked out in the end and I felt better about doing it. The other situation, I actually DID call a cab for two young girls, but it took too long to get there, so I offered to give them a ride instead. Again, no problems and I did my good deed for the day.
25 years ago, I was in college working late and driving home after dark on the highway. My car broke down and I was a few miles away from any exits/civilization and this was before the days that everyone carried a mobile phone. I locked up my car and started walking. I did not put my thumb out and planned to walk the several miles to my exit (not far from my house, so there was no need to look for a public phone). About 200-300 yards into my trek, a car stopped and a few young guys asked if that was my car back on the side of the road and if I needed a lift. I told them it was and that I wasn't going far, but if they could drop me at the exit, I would be grateful. The kid said to me, "You know I'm not supposed to do this sort of thing." meaning picking up strangers, but he said he didn't think it was right to let me walk. If he hadn't seen my car stopped along the berm, he said he wouldn't have stopped.
He ended up driving me to my house and I was able to call a repair shop to tow my car in the following day.
The truth it, we never know for sure who is safe and who is not. But having been on the other end of it, it felt good to be able to help someone else out now. That said, if my wife or daughter offered or agreed to give a ride to a stranger without me or some other trusted and able-bodied man in the car with them, I would probably be livid. It is sad that this is the world we live in, but it is.