I wouldn't pick any year that hinges on one or two great releases, which is why I wouldn't say 1998. Banjo-Kazooie and Ocarina of Time are legendary, but for me they're the only two real standouts of that year (1080, F-Zero X and Mario Party are all good, but flawed in different ways).
Actually, none of the four years I would pick are in the poll. For me, it would be between 1995, 2002, 2004 and 2014 (EDIT: and 1987, too - forgot about that one - Zelda, Metroid, Mega Man and Kid Icarus all began in that one year!).
1995:
Kirby's Dream Course
Chrono Trigger
Killer Instinct
Super Mario World 2: Yoshi's Island
Donkey Kong Country 2
Mortal Kombat 3 (if you're into that sort of thing)
That's one of the best RPGs of all time alongside two of the best platformers of all time (especially SMW2, which was so creative).
2002:
Resident Evil (REmake)
Eternal Darkness: Sanity's Requiem
Super Monkey Ball 2
Super Mario Sunshine
Animal Crossing
Star Fox Adventures
TimeSplitters 2 (not an exclusive, but incredibly fun)
Resident Evil Zero
Metroid Prime
Metroid Fusion
Somehow I never realised that REmake and RE0 released so close together, and they're easily two of the best RE games (along with 4). We finally got Animal Crossing, we got the now-legendary Metroid Prime, and we got a new Super Monkey Ball and a new Mario game on the same day.
2004:
Tales of Symphonia
Donkey Konga
Pikmin 2
Paper Mario: The Thousand-Year Door
Mario Party 6
Metroid Prime 2
Baten Kaitos
Viewtiful Joe 2
Three of the best RPGs Nintendo has ever had all released in 2004, along with terrific sequels to two of my absolute favourite Nintendo games (Pikmin and Metroid Prime) and one of the best Mario Party games.
2014:
Wii Fit U
Donkey Kong Country: Tropical Freeze
Mario Kart 8
Pushmo World
Hyrule Warriors
Bayonetta/Bayonetta 2
Tengami
Smash Bros. 4
Captain Toad: Treasure Tracker
Tomodachi Life
A couple of great downloadable games (Pushmo/Tengami) along with series-best entries for Mario Kart and Donkey Kong. Most people probably don't care about Wii Fit, but I did. Captain Toad was super original, Smash Bros. was strong and Bayonetta kicked ass.
Thinking about it, for me it's probably between 2002 and 2004. The former saw some truly excellent entries in a lot of existing series and the origin of Animal Crossing, the latter was one of their best years for RPGs and also gave me a Pikmin and Metroid Prime sequel.
