For me

Microsoft

1.) Gears of War

2.) Fable

3.) Forza/Dead Rising (not sure)

Sony

1.) Uncharted

2.) Little Big Planet

3.) Infamous (maybe)

Nintendo

1.) Pokemon main series

2.) Zelda with realistic graphics

3.) Pokemon Spin-offs I guess

These are modern, still in progress, franchises only. So no Crash for Sony etc...

Microsoft:

1. Gears of War
2. Fable
3. Forza

Sony:

1. God of War
2. The Last of Us
3. LittleBigPlanet

Nintendo:

1. Zelda (TP)
2. Smash Bros.
3. Mario Kart

Microsoft:
1. Age of Empires
2. Forza
3. Halo

Sony:
1. God of War
2. Ico/SoTC
3. Jak & Daxter

Nintendo:
1. Metroid
2. Super Mario
3. Smash Bros.

Microsoft
1.Fable

thats it.

Sony
1. God of War
2. Wild Arms
3. Ape escape (main line)

Nintendo
1. Zelda
2. Fire Emblem
3. Xeno

4. F-zero (it needs mentioning)

Microsoft
1. Halo
2. Gears of War

Sony
1. Ratchet and Clank
2. Uncharted
3. God of War

Nintendo
1.Zelda
2.Mario
3.Metroid
4. Super Smash Bros

Sony
1. Little Big Planet
2. God of War
3. Infamous

Nintendo
1. Metroid
2. Super Mario Galaxy
3. Mario Kart

Microsoft
1. 'Splosion Man
2. Forza
3. Halo

Microsoft (didn't own one)
1.Halo
2.Project Spark (just a speculation)

Sony
1.Uncharted
2.God Of War
3.Ratchet and Clank

Nintendp
1.ZELDAAA
2.Pokemon
3.Random Mario games (mainly SMBros)

Sony
1. The last of US
2. Uncharted
3. Grand Turismo

Nintendo
1. Zelda
2. Animal crossing
3. Mario golf

MS.
1. Age of Empires

Microsoft

1. Halo
2. Fable
3. Gears of War (eventhough I don't want another sequel for a couple of years)

Sony

1. Uncharted
2. -
3. -

no other franchises that appeal to me.

Nintendo

1. Zelda
2. Mario Kart
3. Starfox

Thread after thread eh?

Nintendo

1) Fire Emblem
2) Mario Kart
3) Metroid (consistantly amazing)

As a franchise, it's hard to decide for Nintendo because many series (like Mario Kart) have amazing and bad incarnations. I couldn't include Mario Party because even though I love 1 & 2, I hate 3-9...

Sony

1) Gran Turismo (bought all my PS consoles when a GT released)
2) Uncharted
3) Drakengard

Microsoft

1) Forza Motorsport
2) Lost Odyssey
3) Gears of War