http://www.appleserialnumberinfo.com/ tells you the year your Mac was made, and a great deal more.

Caveats:

The entered serial number will give, in most cases, the details that were true at the time of the computer's creation. It will not include any modifications the owner has made.
The data is not complete or guaranteed. One of our members reported that the website displayed the wrong details for his processor and speed, and another's MacBook serial number was not accepted.
You are only allowed to enter two serial numbers a day. After that you must wait until the next day or pay. That's why it's a good idea to save a screen capture/pdf or print out your computer's info; you won't have to go back to check something you forgot to make a note of.

The site has Tips and Links sections which are well worth browsing.

External links

Credits

Recommended by Suzanne, with responses by Marvin and Martin, on the Mac-Ministry List in July 2014