To receive warranty coverage on your G-Shock you need to submit a product registration form to Casio. You can either mail in a paper form or register online. It seems much faster and easier to do this online. This link is for the US, but there should be forms for other regions online too. It looks like Casio is currently offering an extra year to the warranty period. Thanks to Rusty for the friendly reminder.

Link (Casio USA only)

Update: European Casio Registration Site - there's no mention of getting an extra year of coverage, but they do have a drawing with prizes.

Casio's G-Shock Registration Form

BTW - When you submit a product registration form you are automatically entered in a sweepstakes with large cash prizes.

From the OFFICIAL SWEEPSTAKES RULES:

NO PURCHASE NECESSARY TO WIN. PURCHASES DO NOT ENHANCE CHANCES OF WINNING. Sweepstakes is sponsored by Equifax Direct Marketing Solutions LLC ("EDMS"), and will be offered in a number of different presentations. EDMS will award the following prizes:

(1) 1st Prize of $50,000;

(1) 2nd Prize of $25,000;

(5) 3rd Prizes of $5,000.

Sweepstakes begins March 31, 2007 at 12:00 a.m. E.S.T., and ends December 31, 2009 at 11:59 p.m. E.S.T.

Enter by completing this product registration or printing a 3" x 5" card with your name, address, city, state, ZIP Code, and the words "$100,000 Give Away VII" and mailing the entry form or card to:

P.O. Box 174404
Dept. MOB01
Denver, CO 80217-4404

Your product registration card may also provide for a method of online entry. Entries must be received no later than December 31, 2009 at 11:59 p.m. E.S.T. and are limited to one per household. Mechanically reproduced entries not acceptable. Not responsible for late, lost or illegible entries.

A random drawing will be held on or around March 31, 2010.