With some of the larger and most influential search engines, the age of a website is used as a key indicator of relevancy. Websites that have been around for a long time are considered more authoritative than short-lived ones. You can use this to your advantage when starting a new website by registering an expired domain.
I use snapcheck.com to locate expired domains for my projects. Try to look for ones that are more than two years old and have some incoming links. This can be a trial and error process as expired domains become more and more popular with domain name resellers, but I’ve managed to manually pick up a few good ones here and there.
Here’s a good tool from webconfs.com that will give you an idea of how old a website is (when it’s first content was published) and ties into the Internet Archive to show you what content was posted there originally.
Tip: Search engines are concerned both with the age of a website and its current length of registration. Consider registering your domain name for five or ten years to maximize its appeal.