Alright, I'll bite. Here we go:
PC - Medieval II: Total War. I really wasn't sure about strategy games when I first picked up Medieval II. I'd heard the series was good and I'd read a bunch of ace Let's Plays, which were what inspired me to try the series. Even when I first started playing (as Denmark, gotta establish Viking rule of Europe once again!) I still wasn't sure about the game until I sat back after playing and realised I'd spent almost an entire day on the thing. Directing the battles had a wonderful sense of scale but for me the big draw was sweeping across the world map, coordinating my armies, diplomats, spies and merchants.
Honourable Mentions - Morrowind, Oblivion, Cave Story, Rome: Total War
PS2 - Kingdom Hearts II. I know people grumble about things like the prologue and Atlantica (which is awesome, an entire world of musicals is kickass) but for me this is one of those sequels that does everything right. It addressed the faults from the first game, namely the clunky combat and occasionally ugly world, made everything more fluid, more fun and ultimately more enjoyable. For me, this is the highest point of an outstanding series of games.
Honourable Mentions - Okami, Final Fantasy X, Final Fantasy XII, Dragon Quest VIII: Journey of the Cursed King, Metal Gear Solid 3: Snake Eater
PS3 - The Elder Scrolls V: Skyrim. I've been a fan of the series since trying out Morrowind ages ago and Skyrim continues the grand tradition of me unknowingly spending 200-odd hours on it. I love the setting, I love the combat, I love fighting dragons... yeah, it's just kinda great.
Honourable Mentions - Mass Effect 2, God of War III, Assassin's Creed II, Assassin's Creed IV: Black Flag, Dishonored, Far Cry 3
PSP - Final Fantasy: Dissidia 012 [duodecim]. I really liked the first game and again, the sequel made everything better. The combat was refined, the new fighters were really cool and a little bit unique (like Laguna) and the way the story played out was a far better system than the previous game's. To be fair, it was mostly an expansion pack sequel, but enjoyable nonetheless.
Honourable Mention - Kingdom Hearts: Birth By Sleep
Game Boy - Pokemon Red. An oldie, but still one of my favourite games of all time. I still play this fairly regularly and even though it has its flaws - glitches, bits of the combat system that are broken, the graphics - it's still one of my favourite RPGs, one of my favourite Pokemon games and definitely the best game on Game Boy.