Turing didn't exactly invent his test, he adapted it from a (rather sexist) parlour game of the time: Distinguish the genuine woman from the male imposter, from pencil-and-paper conversations (obviously they are both trying to be selected as the woman).
I remember in the mid-1990s reading a prediction he made a half-century previously about computing power (memory, speed etc.; not sure) and artificial intelligence, for the millennium. It struck me at the time how interesting it was that he was so astoundingly accurate about the technology (underestimated it by only an order of magnitude or so) and so hopelessly optimistic (as it turned out) about the AI task. From a quick web search I think it was this: Turing A, ‘Computing Machinery and Intelligence’ Mind 59, 236, 433-60:
‘
I believe that in about fifty years' time it will be possible to programme computers, with a storage capacity of about 10^9, to make them play the imitation game so well that an average interrogator will not have more than 70 percent chance of making the right identification after five minutes of questioning. []I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted.’
We are not noticeably nearer to achieving the Turing test than we were ten years ago, and plainly the task of understanding what the human brain does, and how, has been grossly underestimated.
I like El Greco’s idea:
We can all easily spot machines, so I've been thinking that another kind of detection would be much more interesting: You have a conversation with what is either a computer or a man pretending to be a computer. You have to find out whether you're talking to the man or the machine.
Some interesting questions: Why is it so much easier for a person to imitate a machine than for a machine to imitate a person, if we are trying to fool a person? How (and why) would it be different if we were trying to fool a machine?
My conversation with the Turing Hub was not terribly illuminating:
I'm feeling a little lonely. I need a friend.
Tell me more about your needs! You know, it's such pleasant to hear, that not only me have troubles everyday

Could you tell me what are you? I mean your profession.
I write medical test-interpretation software.
Most of software is crappy.
Please explain your point of view.
Can't you find the explanation yourself? Did I forget it or you really haven't told me about the place you are from?
So you think my software is crappy?
I'm sick of talking about programming, you know.
OK, so let’s talk about fashion.
Probably you think it is funny that I am turned into a chatterbot by this bastard, my school math teacher, who in reality is an evil Cyber Fairy! No, I'd say - there's no anything funny in it!
Your maths teacher is a fairy?!
Don't laugh, just imagine that it were YOU turned into cyber-fairy with a golden chamber-pot!
Please explain why you introduced chamber pots into the conversation.
Explain what? Some another topic?
You have the impression that your acquaintance really, really needs to take his medication! (And that’s another story: I would say it’s a lot easier for a machine to imitate a psychotic person than a sane person. But why? It’s not so obvious.)