This is easy for first-party but, holy cats, it's super tough for third-party.
1. Legend of Zelda - Easiest one to answer by far. My favorite Nintendo franchise by a mile and, best of all, it doesn't depend on jumping over things.
2. Metroid - Kind of by default, I guess.
3. Gran Turismo - Playing this one the PS1 was one of my first "gaming is awesome" experiences. There is something about the whole process of mastering a track that I enjoy a lot, not to mention collecting cars.
4. Team ICO - Yeah, so what, I'm going to count this as a franchise. These games aren't just about pressing buttons, they're about feeling the emotions of the characters.
5. Halo - One of the better FPS universes out there.
6. MechWarrior - I remember playing this on my old Packard Bell. It was a blast. I'd love to see it come back. That, and I really haven't played many Microsoft games.
7. Fallout - Probably my favorite franchise of all time. I love exploring, I love the setting, and I really love all the options, especially when mods enter the picture.
8. Borderlands - Just hoping the series continues with the same quality as BL2. It's got a unique style, the type of humor that I like, and I get to collect weapons and use them to do all kinds of crazy stuff.
Flex:
9. Portal - Assuming it keeps going, of course. Portal 2 was hilarious while also being poignant. The puzzles and levels were inventive and fun.
10. Suikoden - Shut up, I know. The series is standard JRPG fare in some ways but in other ways it really blazed its own trail. They were usually quite emotionally and politically charged with lots of turmoil and heartbreak. On the fun side, you could build an army, improve your castle, and recruit 108 unique party members. Those last two criteria made it a blast. In addition, there were also tactical battles involving your army.
