You may have been accustomed to going to Apple.com/support to check the AppleCare status of your Macintosh. This how-to shows you how, amazingly, with three clicks on your Mac, Mountain Lion will display the AppleCare expiration date and even schedule a repair.
Amazingly, you won't need Safari to log on to Apple. All you need is the Finder. Here's how to do it.
1. Under the Apple menu, select About this Mac.
2. Select More Info.
3. On the next window shown, select Service at the top right.
4. Select: Check my service and support coverage status. You should see a page like this with your AppleCare expiration date and other helpful links.
Serial number obscured in this screen shot
Note, in addition, the buttons on the right side to Contact Apple Support and Set Up a Repair. Also, you don't even need to be signed in with your Apple ID for this basic information. Additional services will, however, require a login found on the upper right side of this window. Click on "Why?" to find out more.
For Reference
Back in 2011, I wrote "Special Apple Web Pages to Know About." Under item #3, I provided a direct link to your AppleCare Agreements List. After logging with your Apple ID, you can see a list of all your AppleCare agreements for, say, iPhones and iPads.