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.

When choosing a domain name for your business, there are three rules: short, memorable, and easy to spell. “Short” is pretty self-explanatory. You want the shortest available name that ends in .com. “Memorable” generally means that the name somehow directly relates to either the name of your business or the name of its key product or service. “Easy to spell” is also self-explanatory. If your name is Kodzuleskizicz, you may want to adopt the “Hollywood approach” and come up with a new “stage name” that will be easier to spell. In fact, this last example would be in opposition to all three of the basic rules, right? How do you find the names that are available? The basic tool is the whois lookup, a tool that will tell you whether or not a name is available or already registered to another company or individual. Every domain name registrar will have a whois lookup tool, usually embedded into the home page of their website. At Pelland Advertising, we have a basic whois lookup tool available at the following page on our site: http://www.pelland.com/hosting1.htm The basic idea is that you cannot simply enter an address into a browser’s address bar and assume that a domain name is available simply because a site does not appear. Furthermore, you generally do not want to deal with trying to negotiate the purchase of a domain name which is already registered by another individual. At best, this is usually a costly process that is not worth the time and effort, let alone the expense. What you need to do is to get creative and to keep looking. In almost all instances, any domain name which is based upon a single word in the English language was probably already registered several years ago. The same goes with many of the most logical two-word combinations. Three-word combinations (or hyphenated word combinations or domains that end in anything other than the .com suffix) are far less desirable (and often get too long to be practical). How can you make the whois lookup process more efficient and useful? My suggestion is to try the free tools found at the Domain Tools website. One of the best of these tools is the Whois Lookup and Domain Name Source tool. This tools provides a wealth of useful information, not only when searching for a domain name but for checking the status of an existing domain name. It will show the basic whois records (name, address, phone number, and e-mail address of the registrant, administrative contact and technical contact, along with the nameservers, and dates or original registration and expiration), but it also shows a whole lot more. This additional information includes a screen shot of the site’s home page (along with historical thumbnails), the site’s title and meta description, the site’s DMOZ listing, server and registry data associated with the domain, a calculated SEO score, and the site’s Alexa, Complete and Quantcast rankings. Another very useful tool when looking for the best available domain name(s) is the site’s Domain Suggestions tool. With this tool, you enter your desired domain name or product concept to generate a list of possible names that might be appropriate, showing which ones are available (or already registered) under the .com, .net, .org., .info, .biz and .us top level domains. For example, I just entered the term “lawnmower repair” and found that lawnmowerrepair.com (as well as .net, .org, .info, and .biz) was already registered; however, I was provided with several useful (and available) suggestions, including mowerrepairsite.com, mowerrepairworld.com, mowerrepaironline.com, mowerrepairdirect.com, and others. Useful information? You bet! Take advantage of every online tool at your disposal in order to run your business smarter and more cost-effectively.