who is the greatest chess player of all time?

That's really a difficult question, and one that's been debated for centuries without coming to a conclusion. On the one hand, Paul Keres, with his positional awareness and innovative openings, makes a good case for the #1 spot. At the same time, Bobby Fischer and Valdimir Kramink also dominated during the eras in which they played, and both have very distinct strengths. And of course we can't forget Alexander Alekhine, who was arguably the best defender in the history of the game, and Paul Morphy, whose endgame technique allowed him to grind out a number of impressive victories in close games. I think it's safe to say that each of these players (as well as a few that I did not mention) are all great in their own right.

This has always been one of my favorite questions. I feel Kasparov is. He was the FIDE world Champion or "other" world champion for over 20 years. He was also ranked number one in the world for about 20 years and until last year, when Carlsen exceeded him, the highest ranked player ever!
Anand was one of the greatest too. Carlsen may be, but I fear he may burn out way too soon.
May all your pawns become Queens!

So far as I can see, no-one on this thread is a strong enough player to have a worthwhile opinion on this question.
If humanity had to choose a candidate to play chess against the best alien candidate, the choice is limited: Kasparov, Fischer or Carlsen

It is impossible to compare due to the technology these days. If some of the past greats had the tools avalable today, who is to say how good they would have been?