If it's just consoles and not handhelds, then:
1. Xenoblade Chronicles
2. The Legend of Zelda: Skyward Sword
3. The Legend of Zelda: Twilight Princess
4. Super Mario Galaxy
5. Super Smash Bros. Brawl
6. Donkey Kong Country Returns
7. The Last Story
8. Mario Kart Wii
9. Kirby's Return To Dream Land
10. Wii-series (Wii Fit/Plus/Wii Party/Wii Sports/Resort)-Say what you want, but these games defined this generation in a lot of ways. Plus, for what they are, they're all really well done and tons of fun. Thanks to these games I had a bunch of non-gamer friends who were willing to play video games with me for the first time.
Upcoming Games To Get
Definite: Kirby Star Allies (Switch), Mario Tennis Aces (Switch), Fire Emblem (Switch), Yoshi (Switch), Pokemon (Switch), Kingdom Hearts 3 (PS4), Monster Hunter World (PS4)
Considering: Fe (Switch), Donkey Kong Country Tropical Freeze (Switch), The World Ends With You (Switch), Ys VIII (Switch), Street Fighter V: Arcade Edition (PS4), Kingdom Hearts 2.8 Remix (PS4), The Last Guardian (PS4), Shadow of the Colossus HD (PS4), Anthem (PS4), Shenmue 3 (PS4), WiLD (PS4)
