The Wii's Classic Controller is a good accessory, but is it a necessary purchase to get the most out of your Wii? That depends. If you are going to download and play Virtual Console games, than the Classic Controller is an essential purchase. But if you aren't, you'd best wait until you need one.
For playing Virtual Console games on the Wii, the Classic Controller is great. As advertised, it uses elements from almost all Nintendo controllers, and it definitely works for playing these older games. The classic controller is comfortable, but not as much as the Wii Remote or Nunchuck in my opinion. Also, this accessory won't break from everyday use, unless that includes smashing things with hammers.
Games like Super Smash Bros Brawl are going to utilize this in the future, but for now, the controller is basically good for playing Virtual Console games. And if you own a GameCube controller, you may be fine (although the GC controller is terrible for SNES games). At $20, this isn't going to empty your wallet either, so this accessory is probably worth a purchase.