I'm just going to go with the franchises given by the OP, then add a few more of myself. It's a good way to do it I'd say.
Final Fantasy - It's Final Fantasy VIII for me. Featuring what's still one of the most original plots in the whole franchise, an addictive gameplay system with a prevalent challenge, a kickass score and hours of fun with Triple Triad, FF8 left such a huge impression on me. I've always seen it as a magical game, full of charm despite all its flaws, which have plenty.
Mario - This is quite hard, but I'm going to go with New Super Mario Bros, because I love 2D platforming and those games, despite being extremely easy, provided me tons of fun!
The Legend of Zelda - The Wind Waker. I already explained why in another thread, so I'll rather have you looking for that instead of explaining it here again. :P
Resident Evil - Resident Evil 2. Full of replayability, horrorific charm and awesome plot twists. This game was the epitome of survival horror. Can't begin to think the amount of people that kept dying in the very first thirty seconds because of how the game just throws you into the action like that. xD
Soulsborne - Dark Souls 1. Featuring what's one of the most impressive dungeon designs ever, and a game philosophy that creates a pervasive gameplay system, Dark Souls will forever remain with me as one of the games that renewed heavily my faith in videogames. Not that it was faltering it, but being surprised is always great.
Metal Gear - Metal Gear Solid 2: Sons of Liberty. An amazing step-up from the original, which also features one of the most brilliant subversions and metagaming ever in history. This game was way ahead of its time, and hardly any other game has tried to be as ballsy as this game was.
