Well, like most things in life, the Wii was a mixed bag.
As others have said, we had to wait five years for a game (Skyward Sword) to tap into the potential of the Wii. At least the potential that I was always interested in. That's really a shame. It should have happened a lot sooner. Instead we got lots of Wii Sports type games and dancing games and things that simply are not for me. This was disappointing. Also disappointing, the complete absence of franchises like Pikmin, Star Fox, and F-Zero. In addition, there were things like lack of online play and lack of high definition that just felt more and more dated as time went on, but that was known going in.
As Ian touched on, the Wii got almost nothing in the way of third party support. It's possible I'm crazy, but I think this was the first generation where you couldn't have at least gotten by with only a Nintendo console. You simply would have missed out on too much great stuff elsewhere and the first party stuff had what seemed like worse dry spells than any time on the GameCube or N64. The two years in between Mario Kart and Super Mario Galaxy 2 was a ROUGH time to be a Wii owner.
On the other hand, the Wii has what is probably my favorite library of platformers. As this was the genre that got me into video games to start with, this was a big deal as they had been mostly absent since the N64/PS1 era. (I don't count Ratchet and Jak as platformers.) They came back as a whole this generation, but the Wii has the best of em. The Super Mario Galaxy games were the most fun I've had playing any video game since at least Super Mario 64, maybe ever. The Wii would have been worth it for those two games alone.
In the end, the Wii was another post-SNES Nintendo console. Come for Nintendo's first party stuff, stay for Nintendo's first party stuff. The first party stuff was a little more narrow this time and the third party stuff slimmer than on GameCube, but it ended up being what we thought it would. Which will probably always be okay with me.
Also I'm probably saying goodbye to the Wii with Xenoblade which is the PERFECT way to say goodbye to this system.
EDIT: I forgot to make a "Next Gen doesn't start until I say it does" joke. Oh well.