Overall for consoles & handhelds:
Wii Sports
CoD:4
Gears of War
Mario Kart (Wii & DS)
Brain Training.

If I ignore handhelds I'd take out the last two and replace with Skyrim & AssCreed2... kinda hard to choose though as there are a few that could fit (GTA:V, Uncharted, Mass Effect, maybe Mario Kart Wii or Super Mario Galaxy)

If it just personal influence on me, then:
Wii Sports
Mario Kart Wii
Civilization V
Mass Effect 2
Endless Ocean

1 - The Last of Us: Great story/action

2 - God of War 3: Great story/action

3 - Uncharted 2: Great story/action

4 - Uncharted 3: Great story/action

5 - Pixel Junk Monsters: This game is just addictive!

For the rest of the world, I think some CoD, Gears or Halo games ... maybe even some sports titles should be in the list, or an Assassins Creed or two, GTA IV and V... but I personally am not interested in any of these games

what about Infamous and Ratchet and Clank with their great story/action?  Otherwise this is obviously the best list so far I concede

Wii Sports
Mario Galaxy
Metroid Prime Corruption
Xenoblade
Battlefield 3

Honorable mentions for, Rayman Legends, Gran Turismo 5, Ni No Kuni, Just Dance, Rhythm Heaven, MK 7, Portal, Zelda: Skyward Sword & the 1st 2 COD:MW games.

Wii Sports

By a looong shot no other last gen game comes close to define that gen.

It was the game who brought me back to consoles and for many many others the first video game at all or after TETRIS...

Xenoblade: commonly referred to as the greatest jrpg of last gen

Mario Galaxy: Took 3D Mario to a new level. Also the series most fans want the Wii U to continue

Wii Sports: The game that made motion controls a must have.

Skyward Sword: Although people are divided on whether they like this game, it did bring motion controls to a more core franchise and proved that they could work.

Metroid Prime 3: One of my personal favorites from last gen.

Can you stop having good taste, like, please!!!

1. Call of Duty 4 Modern Warfare
2. Uncharted 2
3. Little big planet
4. The Last of Us
5. Wii Sports

Demon's souls - It started the "souls like" trend that we saw after with Dark souls,dragon dogma,lords of the fallen and bloodborne.

Heavy Rain - it started the interactive "make your choice" movie like "game" trend that we saw with Telltale and quantic dream games.

Mass Effect - It proved that a WRPG didn't have to be a lord of the rings wannabe to be good or acceptable.Too bad the sequels abandoned the RPG elements.

Uncharted - It started the Third person "cinematic" action that we saw with games like TLOU,tomb raider and Resident evil 6.

God of war HD - It started the trend of making HD ports.

I tried once.... Failed, lol.