What one single new first party franchise defined the essence of each console?

[Karlinel]

Nes: super mario bros. Planted the seed for Nintendo global empire.
MegaDrive: Sonic. Embodied better than anyone the "challenger with a 'tude" concept.
Saturn: virtua fighter. Both encapsulates the arcade conversion aspect, and the "rush it and sell it" of Sega's MO.
Psx: wipEout. Style, technology, and basically just evolving on someone else's idea.
Xbox: Halo. Because it was the light at the end of the tunnel.

 

[Deleted member 37233]

Pikmin on Gamecube? I think Luigis Mansion would fit better. It's a new IP and was a launch title.

 

[Mikebison]

PS4 Bloodborne
X1 Lococycle

 

[Ryengeku]

• NES: Super Mario
• SNES: Super Mario
• N64: Super Mario
• Gamecube: Super Smash Bros.
• Wii: Wii Sports
• Wii U: Splatoon
• Switch: The Legend of Zelda
• Gameboy: Pokemon
• Gameboy Advance: Pokemon
• Nintendo DS: Nintendogs
• Nintendo 3DS: Fire Emblem

• PlayStation: Wipeout
• PS2: God of War
• PS3: Uncharted
• PS4: Horizon
• PSP: Grand Theft Auto
• PS Vita: Gravity Rush

• Master System: Alex Kidd
• Genesis: Sonic the Hedgehog
• Saturn: NiGHTS
• Dreamcast: Crazy Taxi

• Xbox: Halo
• Xbox 360: Gears of War
• Xbox One: Forza Horizon

Click to shrink...

I agree with this and add one more.

PSVR: Astrobot Rescue Mission

(Yes, it's an technically an "accessory" to the PS4 but is still practically a new device which plays its own games.)

Edit: GTA for PSP or Fire Emblem for 3DS doesn't count. PSP didn't really have new IPs from Sony first party. It was all iterations of their well known franchises.
And Fire Emblem was popular on the 3DS but didn't begin on it.

 

[Hyun Sai]

Neo Geo : The King of Fighters 98

 

[Deleted member 17210]

Atari 2600 - Adventure
Symbolizing console gaming spreading to do more than just arcade games

Magnavox Odyssey2 - KC Munchkin
Its biggest release and mascot of sorts

Bally Professional Arcade - Checkmate
It shows off the four player simultaneous play

Mattel Intellivision - Utopia
It demonstrates the system's slower but more strategic approach

ColecoVision - Smurf: Rescue in Gargamel's Castle

GCE Vectrex - Mine Storm
It's built into the machine and one of its best games

Sega SG-1000 - Girl's Garden

Nintendo Entertainment System - The Legend of Zelda
Sorry, Mario Bros. didn't originate here

Epoch Super Cassette Vision - Wai Wai Monster Land
A solid effort but, like the system itself, not in the same league as the competition

Atari 7800 - Ninja Golf

Sega Master System - Phantasy Star
It showed off the system's capabilities and was a flagship title

NEC TurboGrafx-16 - Bonk's Adventure
It was the mascot title.

Sega Genesis - Sonic The Hedgehog
Sonic Boom!

SNK Neo Geo - Fatal Fury
It kicked off (way too many) fighting games

Super Nintendo Entertainment System - F-Zero
Mode 7 heaven

Atari Jaguar - Iron Soldier
Some solid polygon gaming in an in-between era

Sony Playstation - Wipeout

Sega Saturn - Panzer Dragoon

NEC PC-FX - Battle Heat

Nintendo 64 - Goldeneye 007

Sega Dreamcast - Shenmue

Sony Playstation 2 - Ico

Nintendo Gamecube - Pikmin

Microsoft Xbox - Halo

Microsoft Xbox 360 - Gears of War

Nintendo Wii - Wii Sports

Sony Playstation 3 - Uncharted

Nintendo Wii U - Splatoon