I am in New Zealand. We have consumer protection in law for individuals under the Consumer Guarantees Act.
We do not have to fill out those purchaser cards to get the warranty. The seller cannot put anything in their sales contract to restrict or reduce the warranty given by the Act.
Suppliers sell "extended warranties" here but they literally are a waste of money and a scam. They are worth getting if the item is bought by a business, because business purchasers are regarded as on a similar footing to the seller, so not covered by that Consumer Act, but they are covered by the Fair Trading Act, which covers pretty much what it says.
A consumer organisation here has put out a list of household items expected lifetimes assuming an average cost, so if yours lasts for shorter than that, you have grounds for a claim. If you got a very cheap one it might be expected to last for proportionately shorter period.
The seller usually has the choice of remedy, not the buyer, so if they choose to fix, and it means you are without the item for some time, it can be a pain.
If it needs several repairs, and this means you are without the item for so much time you effectively cannot use it, you can insist on replacement or refund.
It can take sometime to sort out a claim, and many sellers are not fully aware of their obligations, so try to get out of it, but it works out pretty well overall.
Sorry for the big blurb!