Favorite system as far as the best games and holds the test of time, by far SNES. The 16-Bit age is timeless, many NEW games are made to have this look because it is so timeless. Games from the PS1 and N64 days have some great games but most don't age well due to their early polygon graphic's. I love Zelda Ocarina of Time but man the early polygon graphics look dated today. Yet the ones that used more Pixel graphics hold up better and far as graphics go.
I always had a soft spot for The Atari 2600 just due to it was my first game console.
I also love my Neo Geo consoles, and Turbo Grafx. If I plug one of those in I'll be using it for hours.
As for game exclusives... (many of these games technically have been released on later platforms such as GBA, NDS, nintendo E-store. etc but I'm going by exclusives as of when they came out)
no order. off the top of my head.
1. Super Mario World
2. Legend of Zelda Link Between Words
3. Super Metroid
4. Chrono Trigger
5. Final Fantasy III
6. Super Mario Kart
7. Super Castlevania IV
8. Donkey Kong Country
9. Donkey Kong Country 2
10. Donkey Kong Country 3
11. Mega Man X
12. Mega Man X2
13. Mega Man X3
14. Secret of Mana
15. Earthbound
16. Super Mario RPG
17. TMNT Turtles in Time (ya Gen Hyperstone is similar but its not the same)
18. Star Fox
19. Castlevania Dracula X
20. Kirby's Dream Land 3