Defining "worth it" is the problematic part. Virtually all warranties aren't "worth it" in the sense that it's a bet you're hoping you lose (you're betting your equipment will fail, in which case you collect the cost of repair or replacement), and more often than not, you pay more for the warranty than any service/parts/replacement the warranty covers.
But it's a very different story in terms of peace of mind and how expensive it can be if something DOES happen. Virtually nobody with a mortgage doesn't have homeowners' insurance, and rightly so...the potential for loss can easily be permanently life-changing. Even though homeowners' insurance may be pricey, it's a fool (or a wealthy person who can afford to self-insure) who has a mortgage and doesn't have it.
So it's a numbers game. If the stars (mis)aligned and your battery failed just out of warranty, would you be catastrophically affected or could you scrape up the money to repair it? That's the downside of not having an extended warranty. The upside is not having the payments. So it's a small chance (5%?) of a major expense versus the certainty of a somewhat smaller expense.
Keep in mind that the insurance companies are NOT in business to pay out more than they take in, on average, and extended warranties are some of the most lucrative for them.