The strongest non-champion chess player ever

Korchnoi is a Champion without a crown, he was first sidelined by the Soviet Chess Federation. Then on his difficult path to the world title he faced the strongest in chess history: Fischer, Kasparov and Karpov.

lichess.org/forum/general-chess-discussion/magnus-or-fischer?page=3#30
as i said here
it's hard to compare players who lived in different eras

but a case can be made for each one of morphy, rubinstein, keres, korchnoi, fabi and i am probably forgetting some

Fabiano Caruana's results in the past few years have made him a very good choice.

Shoutout should go to Korchnoi, Rubinstein, and of course various others.

Korchnoi had very good longevity and was the clear #2 for quite some time, but I don't think he was ever quite as strong as Fabiano who for some periods of time (early 2018, mid/late 2014) had the best results of anyone in the world at that time.

Judit Polgar.

Paul morphy

Victor Korchnoi

Carl Schlechter, who tied with Lasker in what was probably a WCC match would be worth a shout alongside Keres, Korchnoi, Rubinstein and Bronstein. I'm discounting active players. Keres and Korchnoi probably have the best case, longevity at the top for these two being greater than the others on my list. Keres lost his best years to WWII, probably followed by political pressure after the war. Korchnoi also struggled from political pressure.

There is also Sultan Khan, an interesting case..
Below is a link to an Agadmator video.
www.youtube.com/watch?v=MSYpwQYXbKE

To add to this, I think we should also consider who people were behind (i.e. who was the world champion at that time) so a lot of players in the Kasparov and Carlsen eras will rank highly here for example. Some of the players who ranked behind these guys would have been the clear best if they were put just a few years earlier.

Basically what I'm saying is some payers might have been a world #1/ world champion in normal circumstances but when you're competing against one of the 2 best to ever touch the pieces (and you're playing them at their absolute peak) it's not really a "normal" time period for competitive chess.

I'll also add that there have been eras where WC matches have been uncontrollably cancelled/delayed (WW1, WW2 etc) so Rubinstein and others didn't always get the chances they deserved and there's nothing they could have done about it. This should be considered as well.