In short, the answer is no.

I was one of four Web developers in a round-table session on broad-ranging Internet topics, presented at a trade association conference in New York this past weekend. In response to an audience question, one of my associates suggested that a longer-term domain name registration played a role in determining a site’s search engine ranking. The rationalization was based upon a presumption that a domain name registered or renewed for single-year terms was an indication of a “fly by night” business. Since it is always our policy to renew our clients’ domains (and our own domains) on a one-year basis, I had to take exception and question the validity of this statement.

Upon my return, I did a bit of online research, and this served to confirm that any suggestion that a longer-term domain name registration has an impact upon a site’s search engine ranking is total nonsense. Apparently this is a piece of misinformation that has been concocted and disseminated by GoDaddy(and often innocently passed along as “fact” by otherwise well-intentioned companies who use GoDaddy as their registrar of choice), in an effort to get people to sign up with them for longer terms. Long-term registrations are in any registrar’s interest because they reduce “churn”, the likelihood of a registrant to transfer to another registrar … either intentionally or as the result of being slammed by an unscrupulous registrar such as Domain Registry of America.

With some registrars, one must be very careful and wary about long-term registrations because they may be, in fact, banking your money (for 10 years, for example), while actually registering your domain on a year-by-year basis, essentially preventing you from transferring your domain to another registrar without suffering a financial loss and the loss of what you presumed was the remaining length of your registration. Do a whois lookup to check. The 10-year registration that you thought covered you through 2018 may, in fact, only be covering you on a year-by-year basis until 2018. In other words, if you transferred now, you may be in for the rude awakening that your domain has only been registered or renewed through 2010. Fortunately, this unscrupulous practice is quite rare.

In summary, there is NO reason to register a domain, or to renew a domain, for more than one year at a time, unless the discount for doing so presents a sufficient incentive in itself. According to Google itself, there is no validity to this recommendation.
http://www.google.com/support/forum/p/Webmasters/thread?tid=00acf87986f79dfa&hl=en
http://www.seoxp.net/?p=384

Domain authority, on the other hand, does play a role in determining search engine ranking. Domain authority is a measurement of the accumulated length of time that a domain name has been registered, but it has nothing to do with the term of registration (or renewal) itself. Domain authority is directly related to the length of time that a website has been in existence and is part of the explanation for why older, established websites often appear higher in search results than newer websites that are otherwise superior in every respect.

Here are a few additional sources of reference:
http://www.webmasterworld.com/domain_names/3334950.htm
http://www.searchengineguide.com/jennifer-laycock/does-registering-your-domain-for-longer.php

My advice is to always question statements of this nature claim to present tips that appear to be a bit far-fetched, in this case the SEO equivalent of urban legends. Take the time to do a search, and discover the truth.