If we exclude McDavid for age reason... (and thinking he will win at least one, the way he is going)
Bure-Hawerchuk-Pavelski-Oates-Stastny-Perreault-Sundin-Iginla-Roenick are some that never won I would look at (maybe not far from that order).
But I could be tempted into drafting Carey Price or Lundqvist, they did win a lot in the playoff without ever touching the cup.
For all the talk about regular season Joe Thornton or Marcel Dionne > playoff accomplishment during their career, that 2 incredible players that were still better in the playoff than most.
If McDavid is available, I would simply pick him without trying to overthink it. But McDavid seem both higher, did it more often and proven that under immense pressure can still deliver, would not mind endeing up with peak Lindros, Bure or Cam Neely obviously, but McDavid seem the clear and easy choice.
I don't think Thornton or Dionne belong on this list. Neither elevated their team to anything. Thornton had a lot more opportunities than Dionne though. I am not sure a great player had a better situation throughout his career who DIDN'T win a Cup than Thornton. Dionne at least you can say he was never on a team that could have won, Thornton was, many times.
Hawerchuk was better in the playoffs than, say, Turgeon or Nicholls. But just by a bit. I would say he fell into a trap of being on some worse teams than them though, and yet PPG he is better than both. It also hurts his PPG that he had a couple of runs late in his career with less points. But does he belong on this list? Meh.
Bure for sure, I'm okay with Oates being there. Pavelski is an interesting choice. 143 points looks sexy until you realize he played in over 200 games. Can't see Iggy or Sundin in there. Iggy in 2004 but that's it, he wasn't drenched with opportunities or anything but he still just has the one run. Roenick is better than Iginla or Sundin, but even in 1992 it was Chelios driving the bus, not him. I don't know if he belongs.
No point in discussing active players.
Middleton and Park seem obvious choices.
Bernie Nicholls and Pierre Turgeon were both good in the playoffs.
How has no one mentioned Peter Stastny?
Stastny isn't a bad choice. 105 points in 93 games, not to mention at least three really productive runs with a good PPG. Never made the finals, that's the only stain against him, but I think he did his part. He reminds me of Perreault in that regards (103 points in 90 games) where he did well in certain runs, but actually took his team to the final once. Also, the Sabres routinely lost to some top heavy teams those years.
Park as others have said is right on the mark. He made several Cup finals, was easily the Conn Smythe winner in 1978 had the Bruins won and played in 161 playoff games with 125 points, great for a defenseman. A darn shame he never won.
Middleton has that great run in 1983, a little lighter after that though. Not that he was bad, just decent. Might have been in the running for the Conn Smythe in 1979 had the Bruins got past the Habs.
I am not seeing it with Nicholls and Turgeon. Nicholls more so though. Like Turgeon no Cup final appearance, although he was close several times. And he did contribute (114 points in 118 games) better than Turgeon (97 points in 109 games).