I dunno about ten, but these ones stand out, to me:
Mario 64 After taking a few bizarre turns with the last few installments of their iconic franchise, Nintendo gets back to basics with Mario 64, introducing Mario, for the first time, in three-dimensional form. The game features a brilliant blend of simplicity (a castle full of rooms that can only be accessed by collecting various numbers of stars) and complexity (each room leads to paintings that, when entered, open up entire worlds in which you can collect said stars). Mario is all but stripped of the increasingly odd powerups he'd had available to him in previous games, but the straightforward options of jumping or running are given a twist, as Mario is given superhuman gymantasic abilities to jump and flip. His moves are dependent on his direction, speed, and immediate environment, so that you can perform a number of different moves based on various contexts with the exact same buttons. This might be the best game ever made.
Prince of Persia: The Sands of Time It would have been all too easy for a game like this to take on an overly cartoonish, Aladdin-like feel, but
Prince of Persia: The Sands of Time manages to maintain a serious tone while simultaneously exhibiting a fairytale-like quality.
Though it sports a story that wouldn't look out of place on the silver screen,
Sands of Time's strongest point is the acrobatic abilities of its titular character. The Prince can run sideways on walls, up walls, kick off walls, hurdle over enemies, do cartwheels, dangle off cliffs, climb ropes and poles, and would be perfectly at home on the men's uneven bars.
As you can imagine, all this jumping around must make for a great many embarrassing (and fatal) falls. Not to worry, however: part of the game's storyline involves the ability to turn back (or slow down) time, allowing you to retry any ill-chosen move, even if it means undoing your own demise.
Super Monkey Ball I would've loved to have seen the meeting where this game was first pitched. "Okay, we've got a monkey, right? And he's in a big plastic ball. And he runs around on floating platforms collecting bananas." The idea was apparently just crazy enough to work, and the result is a game that is as creative as it is addictive. What puts it over the top, though, are the supplemental mini-games, where you can use your plastic-encased marcupials to play pool, race, box, fly, or even bowl. Kudos to Sega for thinking outside the box, and inside a ball, instead.
Super Mario Bros. 3 After the disaster that was Super Mario Bros. 2, you'd think Nintendo would shy away from the head-scratching oddities that sunk it. To the contrary, Super Mario Bros. 3 is, in many ways, even weirder than its predecessor. If you collect a floating leaf, you're given...wait for it...a raccoon's tail, that allows you to...what? Dig through people's garbage? No, it allows you to fly. And something called a "Tanooki" suit makes you look like a giant rodent and allows you to turn into stone, if you can believe that. Somehow, this all made sense at the time. Or maybe our ability to reason was overwhelmed by the off-the-chart coolness quotient of warp whistles. In hindsight, the decision to allow Mario to maneuver between levels on a map was gutsy, and may have been a precursor to Mario 64's castle layout. This is the best game ever made for the NES. 
Intelligent Qube The best game you've never heard of. The concept is simple: you're a man or woman with no discernable features standing on a giant column of cubes floating in oblivion. The ones in front of you roll forward relentlessly. You remove them (and thus avoid being crushed or run off the edge) by setting little "bombs" on the cubes below you, and then detonating them as the cubes roll past.
Throw in some black cubes (which you are penalized for deleting), and green cubes (which, once "captured," allow you to capture all immediately surrounding cubes), and you've got yourself a challenge, and one of the Playstation's most underrated games.
Whew!
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