Okay I've never got Apple care but most of time have opted for Squaretrade warranty and that has been pretty good so far for me. I've question if Apple care is even worth it for Mac-mini considering it is just $799 machine and Apple is asking for another $149 to top it. It is desktop so chances of things going hay-wire with it is less as there is no moving for the device.
What exactly Apple care provides apart from regular repair in case of mal-functioning ? If you've Applecare could you sign-up for some of those one-on-one classes on certain software in Apple store ?
I would say definitely not unless you think you might need the technical support.
The Mini is mostly solid-state. If it's going to fail, it will do so in the first 90 days and you'll be covered by the standard warranty. Other than that, the only parts that are likely to fail are the hard drive and the fan, both of which you can replace yourself fairly easily for much less money than you would spend on AppleCare.
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Do you buy insurance for your car?
I buy it and AC for my systems too.
Whether or not you buy insurance should be a simple math equation, i.e., the cost of the insurance vs. how much it will pay for times the chance of having to use it.
Let's say AppleCare will buy you a new Mini ($800) in the case that it breaks (let's say the chance of that is 5%, to be pessimistic). $800 * 5% = $40. If AppleCare costs more than $40 (it does) then it's not worth it.
Of course you have to also factor in whether or not you can pay for the thing you're insuring out-of-pocket, which is why almost everybody buys car insurance and health insurance, because a loss of a car or a major health problem can easily lead to crippling financial burdens. But hopefully we are all doing well enough here that we can buy a new Mini if we have to.