1. Pokemon: It's my favorite franchise and I've put countless hours into the franchise. The games have great single player and competitive as well.
2. Fire Emblem: Fire Emblem is my second favorite franchise and with the huge amount of unique units, replayability is huge in the franchise.
3. Infamous: It's a fun open world series in which I have enjoyed each game I've played.
4. God of War: The original trilogy was pretty good and I couldn't think of anything better.
5. Minecraft: There's so much you can do in this game and it's fun to play with friends.
6. Banjo Kazooie: It's a dead franchise but it was good while it lasted.
7. Dragon Quest: It's my favorite third party franchise and and of the best RPG franchises that I've played.
8. Assassin's Creed: I know most of the franchise is pretty low quality and repetitive, but it's a guilty pleasure of mine. The open world formula in these games never gets stale to me.
9. Super Smash Bros: It's the best local multiplayer franchise, no contest.
10. The Legend of Zelda: It's the best action adventure series I've played.

1) The Legend of Zelda, Super Mario
2) Ratchet and Clank (favorite platformer), Uncharted
3) Halo and Banjo Kazooie. i guess...
4) The elder scrolls, Grand Theft Auto
5) Final Fantasy, Kingdom Hearts.

1. Legend of Zelda, Super Mario

2. Uncharted, TLOU

3. Halo, Gears of War

4. Mass Effect, Grand Theft Auto

5. Fallout, Fable

Mario
Zelda
Halo
Gears
TLOU
Crash Bandicoot
Warcraft
Half-Life
Doom
Homeworld

Hmm
1. Zelda
2. Pokemon
3. TLOU
4. God of War
5. Halo
6. Forza
7. Destiny
8, GTA
9. Smash Bros
10. Battlefield
Picked these games because i personally enjoy them and they are big sellers.

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.

Nintendo

Legend of Zelda
Fire Emblem

Sony

LittleBigPlanet
Gran Turismo

Microsoft

Banjo-Kazooie (more like the first two)
Halo

3rd Party

Tales
Shin Megami Tensei

Other

Pokemon
Grand Theft Auto

Basically I went selfish and added 6 franchises I love..and 4 that simply have more mass market appeal and/or will help diversify the library. Still probably gonna appeal mainly to Japan though. I call it the Boombox 9000. It plays cassette tapes and comes with stickers. Cuz how cool is that.

Nintendo:

The Legend of Zelda (Never been a fan but the Breath of the Wild looks amazing so it's a must have now)
Smash Bro's (Just fun)

Sony:

The Last of Us (My favourite game of all time)
God of War (One of my favourite franchises, best Hack n Slash series so a must have for me)

Microsoft:

Halo
Forza (Picked it over Gran Turismo as Forza has been the better overall package in the most recent entries)

Third Party:

Grand Theft Auto (Must have)
Battlefield (Even though i haven't enjoyed the recent games in the franchise, Battlefield is a must have due to it's unrivaled multiplayer)

Other:

Uncharted (The best action/adventure series)
Souls franchise

I will create an arcade console that will bring the arcade experience straight back to your home. I will call it the GeoNeo (please don't sue me SNK).

Nintendo:

Mario Kart
Smash Bros

Sony:

WipeOut
Resogun

Microsoft:

Forza Horizon
Killer Instinct

Third Party:

Street Fighter
Crimzon Clover

Flex Party:

House of the Dead
Dance Dance Revolution

Nintendo:
1. Denpa Men - often overlooked but fun little series.
2. Dillon's Rolling Western - it is so fun!

Sony:
3. Patapon - why wasn't this series continued?
4. Journey - this is beautiful

Microsoft:
5. Minecraft - a lot of fun
6. Viva Pinata - great series

3rd-party:
7. Pillar's of Eternity - great RPG
8. Pinball Illusions/Dreams/Fantasies - DICEs best game series!

free for all:
9. Monkey Island - do I really have to explain?
10. Curious expedition - pretty fun!