#6 Shadow of the Colossus

Perhaps the main reason Shadow of the Colossus is so high on my list, is that there's really nothing else quite like it. The setting, story, atmosphere, tone, visual style, even gameplay, all of it is entirely unique to it, with the possible exception of Team Ico's other games. The fights against the colossi are some of the most impressive and well designed sequences in video game history, and the fact that each of them has to be approached differently is amazing. 

Here's a hint for #5

A tactical RPG set in a fictional version of Europe during a great war. 

Lol. Oh you... The Minish Cap isn't the sequel to A Link to the Past.

But wouldn't he actually mean A Link to the Past then? If he's indeed talking about us that is. Though I wouldn't insult that game, in fact the description I gave at #38 is almost a love-letter.

So @Slarvax: A Link to the Past?

Correct.

10. "Son of a Qwark!"
9. This game had the first game of a highly popular series in it. And it was playable.
8. "NOT ENOUGH CASH, stranger!"
7. Who knew a cabby could rise up the ranks of the mafia.
6. A highly popular game that's based on three main cities.
5. This three-quel platformer outdid the sequel, which was already a good game.
4. If you find the secret entrance, you'll go somewhere special.

9: I'm thinking it's something that had the Mario Bros. arcade game in it, but I'm not sure which was the first one. Super Mario Bros. 3?  EDIT: *sees BraLoD's answer* Of course, I'm dumb.

6: GTA San Andreas

5: Crash Bandicoot 3?

Good, good!

Give him a break, he's a racoon with anger issues

But yes, ALttP, not Link's Awakening.

The Legend of Zelda: Link's Awakening as guessed by BraLoD

High up in the list we find the highest placed handheld game, 'The Legend of Zelda: Link's Awakening'. It's a brilliant game, more than worthy of the title "best handheld game ever made", yet sadly often overlooked. The original release on the GameBoy is already sufficient for a place this high in the list, but the 'DX' version on the GameBoy Color a couple years later, sollidifies the claim.

It is a very original game for the 'Legend of Zelda' series, where Link, the same incarnation of Link as the one in 'A Link to the Past' and the newer 'Oracle' games, is shipwrecked during a storm at sea and finds himself on an unknown island populated by people and talking animals, as well as strange foes. As the story goes on, and not even just for a Nintendo game is this one very story-heavy, hints and events allude to a greater mystery that surrounds the island.

This game still amazes me. It is a GameBoy game, but it is one seemingly impossible to have existed on the system. It runs circles around it's "big" console brother released a year earlier in every way, it even has cutscenes, and I am not at all bummed by the fact that I have bought this game four times on three different devices. What's also mostly unknown however is that this game actually pioneered much of the series' mainstays. Mini-bosses, bosses with multiple radically different stages, a guide-character, musical instruments with different songs for different gameplay purposes, fishing, the trading- and the collect-a-thon sidequests all started with this game. A truly amazing game.

From #5 onwards, I doubt that the order of things will ever change.

#4: This game was supposed to be made in a style very different to the unique look the final game had, though a remnant of the original vision can still be seen in the form of the intro-cutscene.

Heh, I could have. But nope, suprisingly I won't and so Wind Waker is incorrect.