This depends on the person. Essentially what you are doing is buying insurance for a predetermined block of time on an item you are purchasing. Companies are no longer standing behind their products as they used to, perhaps due to the complexity and cost of fixing and replacing parts. They have been transferring the burden of dealing with defective products to the consumers as manufacturer warranties on electronics are often valid for just one year from purchase.
Typically, the likelihood of a defect varies according to the Bathtub Curve. Manufacturing defects manifest themselves early and are caught shortly after the item was produced (i.e. when it’s first used). As time goes by, the likelihood of detecting defects drops since manufacturing defects are normally seen early. Eventually the likelihood defects bottoms out. This bottom can last for years. As the item is used, normal wear and tear occurs until one day, towards the so-called end of the item’s life, the item's performance is significantly degraded. During this later period, the likelihood of detecting a defect is greater. Plotted over time, the resulting curve has a "U" or bathtub shape; hence the name.
So, with a one year manufacturer’s warranty in mind, where is your product on the curve and do you need the service plan? It’s hard to say for sure and retail sales people will pressure or scare you into buying one. If the company making your item has a reputation for quality, maybe you don’t need it. If you’re concerned about the item breaking abnormally, then maybe an extended warranty will give you the peace of mind you need. In the grand scheme of things, extended plans only cover you for about 4 to 5 years at most, hopefully ending your coverage near the bottom of the curve where you shouldn't need it. The warranty will offer you limited protection against latent defects: the ones that don't appear right away but that aren't due to normal wear and tear.
So is a plan worth it? The answer is yes if the plan lasts longer than the manufacturer warranty AND if the plan costs a small percentage of the item’s price. If the plan costs 25% or more of the item’s price then you could be better off just buying a newer better item when and if the time comes. Not only will it be newer, but it may even be cheaper and improved. If a 4 or 5 year plan costs, say, 5-10% more than the item, then it’s probably worth it. 10% of $1,500 is $150, making your total price $1,650 ... not that much different for a much bigger warranty!
Sales representatives will often have a catchy phrase like "if anything happens to your item, with this plan you can just bring it back." When they say this, this is your cue to take a deep breath if you need to, to step back, and to not let yourself be rushed into giving an answer. It’s your money, therefore your say. Use a calculator to do the math then give the sales person your answer. You’ll have made a much smarter and informed decision and you’ll feel good about it.
If you are averse to risk, then maybe just go ahead and get the plan anyways for your own peace of mind and enjoyment of the item. You only live once, right? The item will just be more expensive for you, that's all.
It all depends on the person. Just don't forget to read the warranty policy's details first!