Purchasing AppleCare for your Mac actually covers more than just your computer. For starters, everything in the box is covered, including power adapters (for MacBooks), accessories, trackpads, and what many people don't realize, your AirPort devices, even when you purchased them at another time.
A screenshot of what Apple lists as covered devices.
Highlighted is "AirPort."
When you purchase a new device from Apple, you get a one year warranty and 90 days of free phone support. If you add AppleCare to the mix, you can increase that warranty time to two years for iPhones/iPads, iPods, and Apple Watch (non-Edition). For computers (and Apple Watch Edition), you get three years of coverage for the machine itself as well as whatever was "in the box" including power adapters and such. Here's what it says in section 3.2 of the AppleCare Protection Plan terms and conditions:
3.2 Covered Equipment
In addition to the Apple-branded product and accessories contained in the original packaging, “Covered Equipment” includes the following according to your Plan:
(i) Under APP [AppleCare Protection Plan] for Mac, (a) one compatible Apple branded display if purchased at the same time as the Covered Equipment, (b) an Apple-branded mouse, Magic Trackpad, Apple Battery Charger and keyboard if included with the Covered Equipment (or purchased with a Mac mini), or (c) an AirPort Extreme Card, an AirPort Express or AirPort Extreme Base Station, Time Capsule, an Apple-branded DVI to ADC display adapter, Apple RAM modules and MacBook Air SuperDrive if used with the Covered Equipment and originally purchased by you no earlier than two years before the Covered Equipment purchase.
(ii) Under APP for Apple TV, an AirPort Extreme Card, an AirPort Express or AirPort Extreme Base Station and Time Capsule if used with the Covered Equipment and originally purchased by you no earlier than two years before the Covered Equipment purchase.
Here's what that means in English: If you bought a new Mac with AppleCare, and within two years of that purchase you also bought your Mac some treats, those treats and everything in that box (frayed power adapter anyone?) could be covered by the same AppleCare warranty. That includes AirPort base stations and AirPort Time Capsules.
Note that AirPort is also covered with AppleCare for iPad and Apple TV, though not for AppleCare for iPhone.
There's often a debate about the usefulness of AppleCare, but it's frankly a good value when you consider that it covers your Mac as well as a good portion of what you connect to it.