Looks like Super Smash Bros Brawl is having some problems working on a few Wii out there. We've only received a handful of complaints about this here at Kotaku, but it's a big enough problem that Nintendo already has a site set up to deal with the problem in North America.
Super Smash Bros. Brawl utilizes a double-layer disc which has a large memory capacity. A very small percentage of Wii consoles may have trouble consistently reading data off this large capacity disc if there is some contamination on the lens of the disc drive. Nintendo has specialised cleaning equipment that can resolve this problem. (Please do NOT attempt to clean the lens yourself, as you may damage the system.)
Hit the jump for the mini FAQ on the issue:
"How can I get this fixed and how long will it take?"
If you are experiencing disc read errors, please utilise the form below to request a repair order. Nintendo is upgrading inbound and outbound shipping to expedite the total repair process. Specific repair times will be provided as you fill out the repair form below. There is no cost for the repair or shipping. Please note: returning the game to the retail store will not solve the problem. So we encourage users who are experiencing issues with playing Super Smash Bros. Brawl to utilise this repair order process.
"What if I have Virtual Console games or other stored data on my Wii console?"
Due to the nature of this particular issue, you should not lose any of your stored data. In some rare cases you may have to re-download your Virtual Console games from the Wii Shop Channel, but there is no cost to doing so.
Repair Form [Nintendo, thanks to everyone for the tip]