Consoles:
SNES: Nintendo had the best first party games, the best 3rd party games, the best graphics and sound, the best controller...Nintendo was at the peak of their powers then. Just about every great NES game was refined and sometimes perfected on this machine, so I give it props above the NES.
NES: The original. It set the standards for virtually everything else that came after it...only the SNES could best it, IMHO.
Wii: To me, the only reason why it couldn't be the best of all-time was the unfortunate lack of HD in a time where HD gaming established itself as the standard - this cost them the equivalent 3rd party support their market leadership should've commanded. Nintendo's output returned to S-rank form with quite a few of their titles, and they managed to establish new types of gameplay experiences with their motion controller.
N64: The undisputed king of multiplayer in the pre-online console gaming world. The loss of 3rd party support hindered this system, as did the complicated hardware.
GameCube: It didn't do anything the best in its generation - it didn't have the undisputed best 1st party titles, it didn't have the best graphics or the best local multiplayer, it didn't have good 3rd party support, it didn't have the best controller, it didn't create any new experiences...but it still had many excellent games.
Handhelds:
DS: Probably the best game library of all time on any system...and that's discounting the fact that it can play GBA games too. Nothing compares to DS, baby.
GBA: It had many of the greatest hits from the SNES's library, had almost all the SNES' abilities in terms of visuals/sound/control, and had many games that were excellent in their own right, too. Much of Nintendo's great work from 2001 to 2005 can be found here, too.
GB/GBC: Another original, and yet another standard-setter. It was running on fumes after about 1995, up until Pokemon in 1998 - then, the GBC kept the fires stoked with color graphics (finally!), ports of many 8-bit classics, and full GB support. All credit to the OGs.
3DS: It's too early to tell if it will ever be able to match or surpass its predecessors. So far, it's only special for its 3D graphics. Hopefully, the titles will start to come out with the same quality as the DS family it is compatible with!