Is there a device or adapter (similar to the one asked about here for the Xbox 360) to allow me to use my Wii remote and classic controller to control PC games?
The wiimote can be connected to a computer using BlueTooth. There's a tutorial here on how to connect the wiimote to the computer via a program called BlueSoleil, which is often bundled with BlueTooth sticks (it was bundled with mine). The computer should recognize it as a joystick.
Also, this page lists some interesting things you can do with it. Johnny Lee's project are particularly impressive.
Finally, this page on the WiimoteProject site has a more in-depth guide for various ways to connect it, not only using BlueSoleil.
The Wii remote communicates via Bluetooth, so you'll need a Bluetooth receiver.
The games you want to play will also have to be capable of reading input from a Bluetooth device.
GlovePie is a great tool that can be used to get input from a wii remote and use it in an existing game.