Great minds think alike. Reckoning and GBC just posted the players I was thinking of.
Kovalchuk has gone 305 games without making the playoffs, but that should change fairly soon. Luongo's gone 341 games, I think he has a decent shot on Vancouver. Luongo is the best player to never make the playoffs (unless I'm making a major omissions).
The all-time record is probably 734 games for Guy Charron. I don't know much about him, but he seemed to be a pretty good offensive talent for a few years (with consecutive seasons of 71, 82, 73 and 70 points). He was certainly unlucky: he was stuck on the Wings, Scouts and Capitals. Does anybody know more about him?
Olli Jokinen is probably in the top five (in terms of most games played without making the playoffs-- but I don't have the numbers). He's gone 559 games.
In terms of the raw numbers... Vitali Yachmenev played 487 games without making the playoffs. Ron Lalonde, Jack Lynch and Yvon Labre played 397, 382 and 371 games respectively (mostly with the Capitals).
Cale Hulse played 619 regular season games and just 1 in the playoffs.