Nintendo has announced that it is offering to replace the original version of the wrist straps on the Wii Remote with a newer, stronger version. This essentially applies to people who were first to get the Wii, as consoles shipping starting in early December already come with the newer version of the strap.
To see the difference between the two straps, see the following picture.
If you have the original version of the wrist strap, you can order the newer version at Nintendo's Wii Remote Wrist Strap Replacement Request Form. You will need your Wii serial number, as well as a valid e-mail address to order these new straps.
Nintendo expects to begin shipping replacement straps around December 21st. It will take 5 to 9 days for delivery depending on your location. Until then, Nintendo advises you to follow their recommendations listed at the Safety Information for Playing Wii web page.
Nintendo, Wii, Wii Remote, wrist strap