Garmin treats everyone equally concerning warranty service - it doesn't matter where or how you bought it, whether you are the first owner or the tenth owner. There is no warranty card to fill out.
Where they do make a difference is on the matter of free map updates. If, for example, you buy a GPS from an authorized Garmin dealer, and that unit has been sitting on the shelf for 3 years, which means the map CD inside is grossly out of date, Garmin will give you a free upgrade to the current CD when you register the GPSR. They will NOT provide this service for GPSR's that have been purchased secondhand, or from non-authorized dealers such as some (not all) internet retailers. This means, for the most part, that you are on your own if you buy your GPSR via eBay, unless the eBay vendor is a Garmin authorized dealer.
Michael (a Garmin beta-tester)