When asked, "Who is your favourite player?" 99% of the players mentioned have been world chess champions; either Capablanca, Alekhine, Tal, Fischer, etc. My favourite player never to have been the world champion is Akiba Rubinstein.

Did I mention Natalia Pogonina?he

Rubinstein comes to mind, yes.

Don't forget Frank Marshall, Paul Keres, and Viktor Korchnoi.

Paul Keres.

There are many great and sympathetic players that never were really close to win the World Championship, like Charousek and Spielmann. 

Nimzowitsh was never really the number one of his time (he was close but not as strong as Capablanca, Lasker and Alekhine, and in particular he had a very bad score against Capa if i remember correctly). But still his style was extremely interesting, so he is certainly one of my favourites. Rubenstein was indeed a great and most unfortunate player. 

Chucky. He still can try...

The "Praeceptor Germaniae seu Mundi", Dr. Siegbert Tarrasch. True, he was crowned World Champion Tournament Player after winning the 1907 Ostend Chess tournament; but, alas!, he never became World Chess Champion...

Keres and Rubinstein. But Keres is a harder case since Rubinstein failed at St. Petersburg 1914

 Im with you regarding Rubenstein.