New York Islanders:
John Tavares (on his way)
Why? He didn't win a cup with the Islanders, and left as a free agent. The only player numbers retired by the team are cup winners.
Bossy, Trottier, Potvin, Gillies, Smith, Nystrom, Tonelli (the original JT), and Goring (who wore #91 before Tavares)
Granted, he is top 5 at the moment for Goals and Points as an Islander in his career, and 7th in Assists, but the lack of a Cup win, and not playing his whole career on the Island are marks against. MAYBE you can make an argument for Tavares in the team's HOF (which is different than a retired number).
And I just realized this list was pre-Tavares leaving
For the Islanders in general, IF they were to win a cup in the next couple years, you MIGHT consider Bailey and maybe Lee, for being career Islanders winning a cup.