1) Lemieux
2) Jagr
3) Crosby
4) Malkin
5) Francis
6) Letang
7) Barrasso
8) Stevens
9) Apps
10) Pronovost
My list is a little bit weird, so I'll explain my methodology.
First, to be a Top 10 Penguin of all time, you have to be a true Penguin. To me, that means when people think of that player, they think of their years with the Penguins. Maybe not very first, but it has to come up early. Everyone on my list is either a career Penguin or has a decade out of their career that was their "Penguins Decade." Everyone on the list spent at least ten years with the Penguins except Francis and Apps, and Francis is a quintessential 90s Penguin. When you think of Ronny Francis, you think of the Whalers and you think of the 90s Penguins. Apps spent 2/3 of his career with the Penguins, so he's more a Penguin than anything else. This qualification kept Coffey and Murphy off the list for sure, and there would have been an argument for Recchi.
Years played with the Penguins defined the set of players I'm working with, but didn't play any part in the ranking order. That was based on various definitions of greatness.
Definition #1: Elite Player
Elite players could be considered the best forward, best defender, or best goalie in the league at some point in time, either a regular season or a playoff season. Winners of the Ross, Hart, Pearson, Norris and Vezina could be argued to be the best player in the regular season. Conn Smythe winners and leaders in playoff points scored can be considered the best player for a playoff season. The Rushmore guys (Lemieux, Jagr, Crosby and Malkin) all collected a ton of those, though Lemieux the most and Malkin the least. Francis had the most points of anyone on the '92 Cup team, ahead of both Lemieux and Jagr as well as Kevin Stevens, allowing him to slide into the bottom of the "Elite Player" category, at #5.
Definition #2: Great Player
A great player is one of the top players in the league. Top 5 finishes in the Ross, Hart, Norris, and Vezina races are the standard. Too many head-scratchers on a leaguewide basis below the Top 5. Letang has been in the Top 5 in Norris voting twice and Barasso was top-5 in the Vezina twice as a Penguin, so the tie went to the guy who was more consistently above-average. Barasso turned in a couple of below-average seasons. Stevens was #2 for the Art Ross in '92, so he sneaks into the bottom of the "Great Player" category at #8.
Defintion #3: Hall of Very Good
These guys were not necessarily top players leaguewide, but they were quality players and also the best player on the Penguins. Apps was the best Penguin for longer than either Pronovost or Kehoe (who narrowly missed making this list), so he is #9.
Where the ______ was _______ _______?!?
Yes, I left one of your favorite players off. I'm sure everyone wonders where Fleury is, but while qualifying as a true Penguin, he was never elite or great. By the time he was even average, Crosby and Malkin were on the team, so he was never the best Penguin. If you add together his goals saved above (or below) average from the regular season and playoffs, he's literally an average goalie. To me, average doesn't make you the top anything.
Randy Carlyle won a Norris trophy, so he has an argument to be as high as #5, but he was a Penguin for less than a third of his career. Paul Coffey and Larry Murphy have already been mentioned as guys who were great players, but they had even shorter stretches with the Penguins. Each had three top-5 finishes in Norris voting with the Penguins, but everyone thinks of Coffey as an Oiler and everyone thinks of Murphy as either a Capital or a Red Wing.