The first pair of accessories you'll probably want to invest in is another Wii remote ($35) and nunchuk ($20) attachment. The Wii only ships with one set and if you plan on playing with more than one person, you're going to need these. While the nunchuk doesn't require batteries, the remotes do. Replacing their AA batteries can become expensive so we highly recommend picking up one of our favorite chargers, the Nyko Charge Station (in either two- or four-capacity models).
While the Wii can be hooked up to your television right out of the box, we definitely think you should consider upgrading the AV wires that ship with the console, especially if you have an HDTV. The Nintendo Wii Component Cable ($30) will give you a better picture and allow for 480p output.
Now that we've taken care of the basics, it's time to look at a few nonessential items for the Wii. While you don't need any plastic attachments for the system, the($20) is the cheapest plastic add-on around and it comes with a great shooting game (Link's Crossbow Training) to practice with.
Finally, if you're serious about retro gaming, you may want to consider purchasing the($30). The Wii gives you access to a huge library of old school games via the Virtual Console and the Wing controller is the best way to play these older games. The included Wii remote will only work with some of the games, but the Wing's compatibility runs across the board.
For an easy to read, side-by-side breakdown of these accessories, check our must-have Nintendo Wii accessory roundup.