You didn't think we'd get through this list without including a Mario game, did you?
Super Mario Brothers 3 completed the transformation of the Mario franchise from its modest arcade origins into a full-fledged overworld mapped side-scrolling adventure.
Indeed, it was one of the first games ever to include the overworld game mechanic, giving a graphical map to Mario's quest to once again rescue Princess Peach from Bowser.
Each one of the eight lands that Mario travels through has its own theme and nuance, the most unique of which being the Giant World, where all the enemies are, naturally, double or triple Mario's stature.
Mario Bros. 3 gave the intrepid plumber quite a few exciting new abilities: the ability to fly with the Tanooki Suit (didn't know raccoons could fly, but whatever, it's a fantasy world), the ability to swim in any direction underwater with the Frog Suit, the ability to turn into a statue with the Raccoon Suit, the ability to throw hammers with the Hammer Suit (and turn the tables on those f!@#!@# Hammer Bros.), and the mysterious Kuribdo's Shoe, which appears in only one level, but pretty much turns you into God. (For a great laugh, check out Mega 64's hilarious real-world implementation of the Shoe on bewildered and confused San Diego residents.)
It's not just the fantastic level design (each course is full of hidden secret rooms) and the expansion of the tried-and-true Mario gameplay formula that make this entry a gem. There are easter egg secrets that, back in the pre-Internet days, players only knew by word-of-mouth and printed guide. And some of them are still pretty darned hard to get. Example: On specific levels in the first world, if your coin count is a multiple of eleven, and you complete the level with an even number showing up on the countdown timer, you will turn the travelling world enemy into a lucrative coin ship. Another example: achieve a specific difficult coin count on particular levels, and you open up a special "White Mushroom House" that contains a special prize. (I still can't get this done in World 2. Tell me that it's not impossible. I won't believe you.)
Throw in the numerous opportunities for infinite 1-ups, the addition of the power-up cache that Mario (or Luigi) can access from the overworld, and the sheer epic nature of the length of this game, and you have all the makings of a classic. (And let's not forget, the NES cartridges had no batteries with which to save your progress to come back to. We had to earn our victory in one sitting, goddamnit.)
For me, the greatness of Super Mario Brothers 3 can be summed up thus: It succeeds as a short pick-up-and-play diversion, and as a long novel-like adventure that you want to see all the way through.
Super Mario Bros. 3 well deserves its status as an all-time great. There's only one game that can possibly top it...