The following is speaking generally, rather than just for firearm warranties.
In the majority of cases, warranty registration cards exist solely to gather valuable marketing information. While there are a few companies that that require the card to be returned to validate the warranty, most companies do not and some states prohibit requiring warranty registration. Read the terms of the warranty and if it doesn't say the card is required (or if you live in a state where it isn't enforceable), don't worry about it.
That said, there can be certain benefits to registering, such as being notified of recalls or getting extended warranty. You'll have to weigh whether those benefits are worth giving up your info. If you do, all you should provide them is your name, address, date, and name of product purchased for those purposes. They don't need to know how much you make or what magazines you read for that. Another possible benefit to registering is establish the date of purchase without having to dig up the receipt 3 years later. This may or may not be an issue, but some companies will go by the date of manufacture rather than your claimed sales date if you can't provide proof of purchase and didn't register the allotted time. If an item sat a shelf for 13 months before you bought it, you've lost a substantial chunk of your warranty in that time.
Warranty cards and rebates are primarily clever ways to obtain your personal information for direct-marketing use or to rent customer lists out to other vendors. If you want to have a little fun, misspell something slightly or give yourself an honorific and watch what comes in.
For the most part, it's a cost/benefit thing and entirely up to you. Is it worth registering to minimize potential warranty issues on a big ticket item with a long warranty or get recall notification something involved in personal safety (like car seats)? I'd lean towards yes, although I would still minimize the information given. Should you send it in on the $35 toaster? Probably not.
One thing to consider is that if you ever do take advantage of the warranty service, it's likely you'll end up on the same marketing lists.