Who do you think of as the 10 best Chess players never to become the World Champion? I'm not really sure about my list or order, but it would definitely include Rubinstein, Nimsowitch, and quite a few players of that kind of level. What about yours?

Maybe Reti and Larsen?

Just off the top of my head:

Fine, Reshevsky, Bugoljubov, maybe Flohr, Rubinstein (for sure), Nimzo (arguably), Tarrasch (maybe?), Reti, Tartakower, Frederick Yates was no fish, Rudolph Spielmann, George Alan Thomas, and probably Janowski, David.

I'm sure there are a ton more, but these are the ones that always come to my mind.  STRONG players. I mean, unbelievably strong. Just not quite strong enough for WC!

many are there in the list...!!

Rubinstein,Tarrasch,Pillsbury,Zukertort,Maroczy,Reshevsky,Bronstein,Korchnoi,Keres,Schlechter.if-someone-wants-to-include-Nimzovich,i-won't-argue.

http://en.wikipedia.org/wiki/List_of_chess_world_championship_matches

All those who lost the match could be on this list (those who never won)

Well, there have been a number of great players who were not recognized as "official world champions".  My Top Ten would be:

1. Morphy

2. Rubinstein

3. Anderssen

4. Tarrasch

5. Chigorin

6. Korchnoi

7. Bronstein

8. Keres

9. Carlsen (I know he's young, but rated #1 already!)

10. Ivanchuk 

I think Bogoljubov is out of place in a list of "unbelievably strong" players. He did get thumped by Alekhine twice in WC matches, but he was hardly even the strongest candidate available. No doubt Nimzowitsch was more worthy of a shot at the title, and I suppose would have had a much better chance if at that time they would have used some sort of candidates tournament.

One of the great "what ifs" of chess history.

Nice list

In no particular order...

Korchnoi; Bronstein; Fine; Ivanchuck; Keres; Marshall; Rubinstein; Tarrasch; Chigorin; Reshevsky

From what I've read and the games I've played through.

1. Morphy

2. Zukertort

3. Korchnoi

4. Philidor

5. Lucena

6. Greco

7. Tarrasch

9. Edward Lasker

10 Topalov. (But he's going to be)

8. Anderssen

Topalov was already world champion

Rubenstein for sure. I think he would have beaten Lasker in 1914. It's a shame the world never got to see that match. I think it would have been a good one.

If you include "unofficial world champions" here, I'd add Morphy (arguably the most dominant of all time), Zukertort, and Staunton.

I'd also include Flohr, Keres, Fine, Najdorf (I think it was a travesty that he didn't get invited to the 1948 tournament after Fine declined.), and Tartakower.

I'll give Topalov as my tenth, as I personally consider the "classical championship" line to be the legitimate title during the split title era. That said, I suspect that Topa will have to be removed from this list after the 2010 title match.

I must admit I'd never heard of him before. I looked him up on Wikipedia. He seems like someone that would be interesting to know more about.

While it is hardly conclusive, the videos of Topalov's manager apparently sending him signals from the gallery make me suspicious that even his current ranking may be "enhanced."

Topalov is certainly one of the top players never to be World Champion. I cannot emphasize enough that he has never been the World Champion.

Korchnoi, Keres, Pillsbury, Rubinstein, Tarrasch, Larsen, Geller, Stein