Alexa.com is one of the big players in the search engine business that has been around since 1996. Although it isn’t as large as Google.com or Bing.com, it plays a unique and important role.
Specifically, Alexa openly gives detailed site metrics and traffic reporting with its search results that a large number of tools and people use when evaluating a Web site. Also, Alexa has an extensive set of APIs and Web Services that are commonly used by a large number of third party search tools
Alexa is a subsidiary of Amazon.com, and so in my opinion it is likely to continue to grow in stature along with Amazon. As well, it has close ties to both Google and the Open Directory Project, which are both prominent players in the search world.
So bottom line here is that getting your site into Alexa and having it properly catalogued is pretty important.
But the process of claiming your site in Alexa is not easy if you are trying to claim a WordPress.com site. There is a lot of mis-information out there as well as incompletely written instructions (including on the Alexa FAQ site itself). I found this out the hard way today.