In this scan at Blue Skies and Nintendo, it lists the Nintendo Power Awards (originally awarded with a "Nester"). The Nintendo Power Awards were reader-picked games for the best games of the year. For those too lazy to click on the link, here are the winners.
1988: Zelda II: The Adventure of Link
1989: Teenage Mutant Ninja Turtles
1990: Super Mario Bros. 3
Super NES Era
1991: Super Mario World
1992: Street Fighter II: The World Warrior
1993: Mortal Kombat
1994: Donkey Kong Country
1995: Chrono Trigger
Nintendo 64 Era
1996: Super Mario 64
1997: GoldenEye 007
1998: The Legend of Zelda: Ocarina of Time
1999: Donkey Kong 64
2000: The Legend of Zelda: Majora's Mask
2001: Super Smash Bros. Melee
2002: Metroid Prime
2003: The Legend of Zelda: The Wind Waker
2004: Metroid Prime 2: Echoes
2005: Resident Evil 4
2006: The Legend of Zelda: Twilight Princess
2007: Super Mario Galaxy
2008: Super Smash Bros. Brawl
2009: New Super Mario Bros. Wii
And now for commentary.
1988: Despite The Legend of Zelda pre-dating Nintendo Power, electing Zelda II seemed like a fine way to introduce the award-winning Zelda series.
1989: If this doesn't say anything about Nintendo Power's demographic at that time, I don't know what else will.
1990/1991: For two years, Super Mario defeated Bowser and won the Nester.
1992: Despite The Legend of Zelda: A Link to the Past being released that year, it regrettably lost to an arcade port (the first iteration of Street Fighter II). Take heart: Link to the Past sold well and is remembered as one of the best video games of all time, certainly of the SNES.
1993: An embarrassment considering the censorship of Mortal Kombat on the SNES...they changed the blood to "sweat".
1994: Donkey Kong Country broke the Donkey Kong series out of the Arcade Ghetto and brought DK into his own canon.
1995: One of the best SNES RPGs ever.
1996: Super Mario 64 proved that 3D games had a future. It was fun to play, had excellent music, and still holds on today as a great game, even though its polygons are dated. After SM64, Nintendo-published titles won for the next eight years...
1997: For many, it was the first FPS shooters they ever played. Then Halo: Combat Evolved came out and the former N64 players were switched over to Xbox.
1998: No argument here.
1999: Arguably, you could say that Donkey Kong 64 was a cheap knockoff of Super Mario 64 and not worth saying another word about. Other reasonable games came out during 1999, but this was Nintendo Power and Nintendo-published titles took absolute presence over third-party titles.
2000: The Legend of Zelda: Majora's Mask pushed the N64's capabilities and was one of the oddest Zelda games ever made. While it didn't kill the basic formula, it did introduce new play mechanics. Some people hated the new changes and the odd storyline, others loved it. The lovers won.
2001: SSBM was a radical change from the original SSB. Some people loved it. Some preferred SSB.
2002: Notice that Super Mario Sunshine didn't win.
2003: Despite the art change, the new Zelda game was surprisingly fun, somewhat dark, and featured Link sailing the high seas in a talking boat.
2004: It's depressing when sequels win (then again, Halo 2 was released that year for the Xbox)
2005: Resident Evil 4 was an award-winning game and came out only for the GameCube. Unfortunately, it came a day late and a dollar short to save the GameCube...and a PS2 port came soon after.
2006: A launch title for the Wii but one of the last GameCube titles, Twilight Princess wasn't quite a groundbreaker like Ocarina of Time, but it was still good.
2007: Again, no argument here.
2008: Despite the fact that it should've been released earlier and the fact that it was an improved SSBM, SSBB was amazing.
2009: NSMBW should've been one of many great games of 2009, but the fact a side-scrolling Mario game won was depressing, or awesome, depending on who you talk to.
All of the non-Wii/GCN games listed here ARE available on the Virtual Console (except Mortal Kombat, Chrono Trigger, Goldeneye 007, and Donkey Kong 64) so go play!