If we are talking about great players that could fight, then Red Kelly might be at the top of the list. Andy Bathgate & Harry Watson can be added as well.
I don't know how the posters are defining 'fight'. If its the best technically sound fighter, then Red Kelly again would be near the top. Kelly was a Golden Gloves Champion while at St. Mikes and after his initial beatdown of Vic Lynn of Toronto in the 1950 semis, Kelly was very seldom challenged. Kelly also wasn't a hothead so that's another reason why he didn't fight as much.
When Maurice Richard fought, it was with much passion and hate and of course he had to have some fighting skills. Gordie Howe showed his fighting skills in the Lou Fontinato fight but not much before and certainly not after that bout.
Bobby Orr has been named here a few times and it seems that, like Gordie Howe, that posters are merely repeating what they have read or heard and just automatically assume that Orr was one of the top fighters. Orr as a fighter can be an interesting debate though.
'Jiggs 10' says that Orr got into 3 or 4 doozies as a rookie but doesn't say who those fights were against. I can presume that two of those were Ted Harris and Orland Kurtenbach - two pretty tough guys. Orr won a decision on Harris but Harris was really fighting with one good arm. Derek Sanderson commented on that fight and said he moved in because he sensed Orr was tiring and that Harris might start to reverse things. Orr had a draw at best against Kurtenbach. But just to hold your own against big Kurt meant that you had to have some fighting ability.
But these were not really doozies in the sense that Orr destroyed his opponents because he didn't.
As for Orr fighting Pat Quinn as a rookie, then that is another piece of misinformation that keeps getting repeated and repeated. First of all, Quinn was not in the NHL when Orr was a rookie. Orr and Quinn did fight late in Orr's third year in the league (when Quinn was a rookie) but it was very brief - each kicked each other in the pants then all the Bruin players jumped in, which they always seemed to do.
It was in Orr's fourth year that he fought Quinn in Boston. Quinn was winning that fight until Fred Stanfield pulled Quinn down from behind with Orr on top. So, people say Orr won but it wasn't a dominant victory if you even call it a win.
When Orr fought, it wasn't so much a skillfull fistic demonstration but rather sheer aggressiveness and determination when he fought. Orr punched linesman and opponents - it didn't matter to him, he was so full of fury when he fought. You can see all this is the fight videos.
Orr shouldn't have been fighting of course. But when Orr did fight, his teammates almost immediately jumped in. I don't know how many people know this but the 'third man' rule in was put in specifically because of the Bruins' brawling, well before the 'Broad Street Bullies' used their cowardly gang tactics.
I just finished helping on a book about Bobby Orr that should be out this fall and of course I recommend you guys getting it to learn more about Orr especially and the Bruins from that era.
One thing that wasn't in the book but is revealing about Orr and his fighting was that when he was 14 years old and playing for the Oshawa Generals, he was beaten up in a fight with a 19 year old player from the Brampton 7ups for no apparent reason. ( A teammate of the Brampton player told me this). I think, that after that fight, Orr was determined not to let that happen to him again. That explains partly why Orr fought so much.
Others did challenge Orr after his rookie year and Orr lost two decisions to Rosaire Paiement. But usually, Orr did well in his fights because of his temper and his aggressiveness and his athletic ability (and his Big Bad Bruins teammates).
I'm just trying to set the record straight about Orr's fights and his battles with Quinn which seem to be misinterpreted.