Ice Climber is charming and innovative but some terrible execution kept it from being a true classic.
The Bad: All above fall short due to terrible controls/physics.
For an early NES release Ice Climber was fairly innovative in its concept: while most of the games at the time used to stick the player to a single screen this one proposed a vertical scrolling platform action. (By the end of the same year another game featuring a certain plumber has definitively settled the horizontal course to the entire platformer genre, but that's another story...)
And that premise alone would make an interesting game... let alone the cute Eskimo kids (both on the same screen in 2-players mode if you want to) and some neat levels design, everything adding up for a terrific game. Right? Well, unfortunately not.
Ice Climber's cool ideas were wasted due to nothing less than terrible physics and controls. You can jump like 10ft high but no more than 1ft long; you'll bounce walls helplessly when trying to hang over a 10-pixels-wide piece of ground--and die a lot since the plat you were above a second before ceased to exist as you went further; you'll go THROUGH the edges of plats--or other objects for that matter--due to some ridiculously loose hit detection.
You got the picture. A platformer that doesn't manage to give you full control of your character can be just as infuriating and frustrating as this one.
People sometimes try to sell games as "classics" just because they like it or because they're old enough; Ice Climber can more than often be the case, but in fact it doesn't belong the breed because it lacks what it takes to be such a game.