The WiiTracker: http://nintendo-scene.com/wiitracker is a database application designed to catalog Wii Serial Numbers and cross reference them with known data about the hardware inside a Wii console. The results of this data is automatically analyzed by the application to allow those looking to purchase a Wii, or considering modifying their Wii to find out exactly what is inside their console before they open it.

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Wii Serial Number: This is located on the large sticker on the bottom of the Wii (when standing vertically). It's 11 digits long and made up of letters and numbers. This number is unique to each and every Wii console and it also contains valuable data about the console.

Wii Copyright Year: This is located on the top left of the large sticker on the bottom of the Wii console (when standing vertically). Since the Wii does not have a manufacturing date available the copyright year is the next best thing. Tracking that against the serial number could provide some insights.

A Rough Guide to which serial number ranges represent which hardware

North American Consoles (USA, Canada, and Mexico) have 3 prefixes LU1, LU3 and LU5. LU1 production seems to have stopped LU3s are still produced in small quantities and LU5s seem to provide most North American production.
LU1
LU10000xxxx - LU10580xxxx D2A/DMS/D2B without cut pins
LU10580xxxx - LU10613xxxx (gamble) Could have D2B or could have D2C
LU10613xxxx - [And Higher] Have D2C Chips

LU3
LU30000xxxx - LU31539xxxx D2A/DMS/D2B without cut pins
LU31539xxxx - LU31546xxxx (gamble) Could be safe could have cut pins
LU31546xxxx - LU31867xxxx Have D2B Chips with Cut pins
LU31867xxxx - LU31874xxxx (gamble) Could have D2B with cut pins or could have D2C
LU31874xxxx - [And Higher] Have D2C Chips

LU5
LU50000xxxx - LU51522xxxx D2A/DMS/D2B without cut pins
LU51522xxxx - LU51634xxxx (gamble) Could be safe could have cut pins
LU51634xxxx - LU52386xxxx Have D2B Chips with Cut pins
LU52386xxxx - LU52390xxxx (gamble) Could have D2B with cut pins or could have D2C
LU52390xxxx - [And Higher] Have D2C Chips

European Consoles - have one Prefix LEH1 though the serial number length ranges from 11 digits to 12 digits.
LEH1000xxxxx - LEH1231xxxxx D2A/DMS/D2B without cut pins
LEH1231xxxxx - LEH1233xxxxx (gamble) Could be safe could have cut pins
LEH1233xxxxx - LEH1347xxxxx Have D2B Chips with Cut pins
LEH1347xxxxx - LEH1356xxxxx (gamble) Could have D2B with cut pins or could have D2C
LEH1356xxxxx - [And Higher] Have D2C Chips

South Pacific Consoles - (Australia and New Zealand) have one Prefix LAH1 though the serial number length ranges from 11 digits to 12 digits.
LAH1000xxxxx - LAH1014xxxxx D2A/DMS/D2B without cut pins
LAH1014xxxxx - LAH1016xxxxx (gamble) Could be safe could have cut pins
LAH1016xxxxx - [And Higher] Have D2B Chips with Cut pins

Japanese Consoles - LJF1 and LJH1
--Not enough info to provide a valuable estimate--