Well, it's the only console I've ever bought & sold twice...so there's that. I was a huge fan of Nintendo growing up with the NES, SNES, N64, and to an extent, the Gamecube. The Wii is pretty much where they lost me.
I waited in line for the launch and after the thrill of motion controls wore off (Which didn't take long), it was used for Wii Sports or gatherings and not a whole lot else. It had some really good games, great ones even (Like some of the ones mentioned in this thread so far), but those were generally in spite of the console, not because of it. I still think Boom Blox was one of the very few games where I thought to myself, "This just wouldn't be as fun without motion controls."
It felt like for every great exclusive Wii game, it was missing out on 3 great 3rd party games that were on the 360 and PS3. I mean, I couldn't imagine having a console last gen and not getting to play any of these:
Bioshock series, Mass Effect series, GTA IV & V, Fallout 3 & NV, Oblivion & Skyrim, Just Cause 2, Orange Box & Portal 2, RDR, Batman Arkham Asylum & City, Dark Souls 1 & 2, Assassin's Creed Series, Borderlands Series, Xcom Enemy Unknown & Within, Dead Space Series (There was Extraction, but even that went to the PS3), Deus Ex: HR, Street Fighter/Soul Calibur/Tekken/Blazblue/Virtua Fighter/Mortal Kombat Entries, Battlefield games, Dishonored, Dead Island & Riptide, Dirt Series, Skate Series, Dragon Age: Origins, Vanquish, Bulletstorm, Darksiders 1 & 2, Some of the COD games (Not that I got into 'em too much, personally), Saints Row 2-4, Mirror's Edge, and a bunch of arcade/indie games like Super Meat Boy, Minecraft, Terraria, Spelunky, Dungeon Defenders, Braid, etc.
I had a PS3 and a 360, so my apologies if a couple of those were exclusive to one or the other. But considering the Wii missed out on those, that's rough. I feel like the Wii is pretty decent if you take it by itself, but it starts to crumble when compared to last gen as a whole (Especially if you consider it was sub HD and the online was lacking, at best). I'd be willing to say it makes for a great complimentary console, but there's no way I would've had it be my only console last gen.
I can understand why some would love it, but it just didn't resonate without me.