I call my system the Merrycase! (name is provisional, of course)

I tried to be as balanced as possible, looking to compensate for most genres rather than just picking what games I would have just preferred:

-> Two franchises from Nintendo:

· The Legend of Zelda. To satisfy action/adventure in its pure, unadulterated state, while actively having a recognizable icon to exploit at will.

· Fire Emblem. To have that specific SRPG in-house that challenges the competitors but also finds a place in the market.

-> Two franchises from Sony:

· Infamous. Because not only it is an amazing franchise, you can also ride the Superhero crazy with it these days, and make multiple Marvel/DC spin-offs with it.

· LittleBigPlanet. To grasp creativity and replayability, as well as user-created content and multiple entries that would continue to evolve.

-> Two franchises from Microsoft:

· Gears of War. Frenetical action with guts and gore, that pushes both enjoyable, bloody fun campaigns while also superb online content that rememorates the good old days of Unreal Tournament.

· Fable. Charm and entertaining RPG; while not as hardcore as other franchises, its own identity gives place to a different in-house experience.

-> Two franchises from third-parties

· Final Fantasy. Longstanding tradition, amazing list of videogames, brand appeal and just plain amazing games altogether. This part also satisfies the hardcore RPG demand Fable cannot.

· Fallout. Another franchise who has become worldwide known and produces some amazing, albeit not up to everyone's taste, games with tons of replayability and charming universes to explore.

-> Two flex franchises:

· Dragon's Dogma. More RPG goodness for the system, and the possibility to work with both the branch of singleplayer-heavy sequels and exploit the online-oriented games (aside from what Final Fantasy already has) to grasp that segment of market.

· Project Gotham Racing. To give driving race fans a superb franchise to play with.

EDIT: On second thought, I went a bit too overboard with RPGs. Oh well.

Two franchises from Nintendo (The Legend of Zelda, Pokemon)
Two franchises from Sony (Uncharted, God of War)
Two franchises from Microsoft (Halo, Forza)
Two franchises from third-parties (Crash Bandicoot, Dark Souls)
Two flex franchises from whichever categories you want (Tekken, GTA)

1. Super Mario
2. Pokemon
3. Gran Turismo
4. Uncharted
5. Halo
6. Minecraft
7. GTA
8. Call of Duty
9. The Legend of Zelda
10. Fifa

My list is made with success in mind, not personal preference.

edit: forgot Fifa

1. Pokemon
Simply put, Pokemon is Nintendo's greatest franchise. the hardcore fans may dispute, but Im not sure there has ever been a franchise that has been able to remain at this level of quality after over 20 years. The new mechanics they introduce feel refreshing without messing up the game's entire formula. I couldnt live without it.

2. Super Smash Bros.
Does this count? It is a crossover game. Anyways, Smash is great as a party game and a fighting game. and its one of my all time favorites

3. Kingdom Hearts
KH is almost entirely represented on Sony's consoles, so im counting it.

4. The Last of Us
great story, likable characters.

5. Sunset Overdrive
an open world game that doesnt focus on being realistic? mutants with bright colors? insane parkour that doesnt even try to obey the laws of physics? its all here, and it is beautiful

6. Forza
gotta have a racing game

7. Grand Theft Auto
Rockstar needs no explanation. every other company needs an explanation for why they cant keep up with Rockstar

8. The Elder Scrolls
no specific reason, its just an enjoyable franchise.

9. Stardew Valley
farming games are just so relaxing and enjoyable. then when Harvest Moon, the big name in the industry took a shit on us, Stardew Valley showed up, ditched the unnecessary crap that nobody liked, and amplified everything we did.

10. Splatoon
a breath of fresh air for shooters,

Nintendo
- The Legend of Zelda (My favorite Nintendo franchise and home of my favorite video game of all-time (Skyward Sword))
- Fire Emblem (To get my strategy RPG fix, and another one of my Nintendo favs.)

Sony
- The Last of Us (One of the best franchises to come out of the 7th gen and something that's a must have for PlayStation owners.)
- InFamous

Microsoft
- Halo
- Fable

Third Parties
- Final Fantasy (To get my action RPG fix.)
- Sonic the Hedgehog (My favorite video game franchise overall. I'll always stand by the Blue Blur.)

From whatever I want
- WWE 2K (Wrestling Fan)
- Super Smash Bros. (It's Smash Bros.)

Love the diversity here! Lots of unique picks!

Ok. I'll qualify this briefly by saying I won't include any one offs that had franchise potential, but were never continued.

Halo - I'm just a total fanboy here, I need my Halo

Forza Motorsport - Best racing game on the market

Super Smash Bros - Just a damn good time with friends

Xenoblade - Tbh, I've never played any of these, but it's one of the only games that interest me on Nintendo platforms these days. They look pretty great

Uncharted - Fantastic spectacle action/adventure thrill ride

God of War - Killing gods is good for society. It's also a good time

Mass Effect - One of the best SciFi Universes ever created

Witcher - Because CDPR just made what is objectively the best, most complete game ever made up to this point in time

Red Dead - Only just recently rose to prominence, but it's obviously going to be a huge franchise moving forward, and tbh it's easily my favorite Rockstar game. I love the setting, and interestingly enough it's really your only choice if you wanna play an awesome western. Nobody else is even trying.

Total War- I could have actually given the last spot to quite a few different franchises, but for the sake of variety, I'll go with Total War. Love me some good strategy games, sometimes they're all I play for weeks, and Total War has had quite a few of the absolute best

Super Mario
Zelda
Minecraft
Halo
The Last of Us
Gran Turismo
Call of Duty
GTA
FIFA
Pokemon

but that's not my personal taste. Ithink it's the best for industry overall.

My personal choice:
Super Mario
Donkey Kong Country
Gears of War
Forza Motorsport
The Last of Us
God of War
The Elder Scrolls
The Witcher
Fallout
Portal

1) My list based only on future games, not the current library.

2) lets consider all those franchises become active. I know I can wait for Portal 3 for ages.

3) Uncharted already over after DLC. So that's why I do not included this franchise in both lists.

Variety and availability to all audiences makes a succesfull console IMO. So here are my picks: 

1. Pokemon (Nintendo) - Any console with Zelda, Pokemon, Uncharted, Halo, FF and GTA is bound to sell incredibly well. All ages. 
2. The legend of Zelda (Nintendo) - Best action/adventure with rpg elements franchise. All ages. 
3. God of war(Sony) - Best hack and slash. Mature audience. 
4. Uncharted (Sony) - Another one of the best action/adventures. All ages. 
5. Halo (Microsoft) - Popular FPS with very popular multiplayer. All ages (I think)
6. Forza(Microsoft) - One of the best racing games to add variety. All ages. 
7. Final Fantasy (Square Enix) - Best and most succesful RPG franchise. All ages. 
8. GTA (Rockstar) - Popular as hell, big hook sandbox game. Mature audience. 
9. The Elder Scrolls (Bethesda) - Western RPG to balance with FF. All ages (I think) 
10. Souls franchise (From Software) - Because quality games are just quality games.  M for Must play. 

• Nintendo
  • Mario platformers, Smash Bros. One of the best platforming franchises and my favourite local multiplayer series.
• Two franchises from Sony
  • Uncharted and The Last of Us. This was a very close call. Ultimately though, I just slightly prefer Naughty Dog's two main franchises over Sony's other franchises.
• Two franchises from Microsoft
  • Uhh, I don't really care much for any of Microsoft's first party franchises. I suppose Halo and Forza.
• Two franchises from third-parties
  • Souls, Final Fantasy. Easily my two favourite series of video games ever.
• Two flex franchises from whichever categories you want
  • The Legend of Heroes, Tekken. Both are among my favourite series. The Legend of Heroes has a lot of niche appeal, and Tekken is in my opinion the best fighting game franchise ever.