1 - Playstation 3
Mass Effect (2?)
I would say Mass Effect 2 is my favorite game of all time, but it's hard for me to separate series like this into individual games. Normally that wouldn't be complicated, but since ME1 was originally an Xbox exclusive and didn't get ported to PS3 until after the trilogy was concluded, it's an unusual situation if I want to be technically accurate to my own preference AND follow the rules of this list...
Nevertheless, that's my number one answer. Everyone here has heard enough about Mass Effect, I'm sure, so I'll forego the explanation of why it's my favorite.
The majority of my top games are on the PS3, so I will have to shimmy down the list a bit to get to...
2 - Playstation 2
Shadow of the Colossus
This was a rather agonizing choice. There are as many excellent games here as there are on the PS3. This came down to either SotC or Persona 3, and I can't really say why I picked one over the other. But Shadow of the Colossus is just such a one-of-a-kind game, delivering an experience that I knew I would treasure forever long before I even finished the game. It doesn't have the endless replay value of many of my favorite games, but that almost doesn't matter when it leaves such a powerful and lasting impression.
Now it's going to get a bit muddy, as these are the only two platforms I have ever owned a large number of games for. I think the final 3 are going to be pretty interchangeable, but my next pick will have to be...
3 - Gamecube
Metroid Prime
This is the only game I ever owned for the Gamecube, gifted to me with the system by my stepbrother. It's plenty reason by itself to own this console anyway. I've never even played any other Metroid game, so perhaps my perspective isn't very informed, but I certainly don't know any other game that does the exploration thing quite so well. In fact, exploring Tallon IV is such a focus of the game that combat seems secondary.
A lot of people praise Dark Souls for it's oblique way of presenting the lore and the story in a way few other games do. If you ask me, Metroid Prime does this far better than Dark Souls. In DS you will likely miss most of the backstory and, indeed, what even actually happens in the game. In Metroid Prime the lore is given to you just as briefly and indirectly, but still manages to weave itself into the experience effectively. You are not going to go through this game with no clue why you are doing what you're doing.
For it's expert integration of fun exploration, surprisingly interesting boss fights, and lore into one cohesive whole, Metroid Prime is easily the best Nintendo game I've ever played. Which brings me to...
4 - PC
Heretic
You've all heard of Doom. Heretic is like Doom's little brother. It's younger, so it's always been in the shadow of it's older, better-known sibling, but it learned from it's brother's mistakes and lived a quieter, more fulfilling life. Until Heretic 2, at least.
Heretic is an early FPS, like Doom, set in a fantasy world overrun by demons, under the dominion of D'sparil, youngest of the three Serpent Riders. It was made by id software a couple years after Doom and added things like the ability to look up and down, as well as better graphics and far better level design. Doom may have a more visceral feeling of dread with its dark hallways and hideous monsters popping out at you, but Heretic is more streamlined and just more fun to play. It's less about the fear and gruesome visuals than being a solid shooter. It has, I think, smoother mechanics than most early FPSs, and is more focused and confident than it's predecessors.
I'm not sure why it never got the fame or notoriety of Doom, but it's a much better game in any case.
Now, the only other game platforms I've owned are the Sega Genesis (my first console ever), the Gameboy Color, and the original Playstation. Which will it be...
5 - Gameboy Color
Pokemon Gold
I only owned the first two generations of Pokemon, though I played the third once on a borrowed GB Advance. Gold and Silver was definitely the best generation of the three. The first generation was, of course, an instant classic, just a great, addictive game with RPG and collection elements up the wazoo. Gold and Silver was just more of the same with a bunch of new features, mechanics, and collectables. It was exactly what it should have been; it didn't try to revolutionize a formula that it knew was already a winner, and it wasn't old enough yet that it had to get radical in trying to breath new life into itself. It was just a pretty much perfect game.
This was a good twist, OP. I had fun with it, thanks.