I just answered this question for someone on Linked In and thought it would make a good blog post
Is there an SEO advantage to having multiple domain names pointing to the same sight? (sic)
Google will penalize you if you have duplicate content under two or more domain names, but if you have a domain you use for a print or tv campaign, and use Google Analytics or another web analytics program, you can set up to following situation to track the campaign.
Use the Google URL Builder to create a URL that will work with Google Analytics.
Another thing to remember is the www.primarydomain.com and primarydomain.com are different domains in the eyes of Google, so make sure you pick one and stick with it for all your linking, SEO, and other online marketing. You can also set the primary domain in Google Webmasters tools.
SEO is more than just domain name, so make sure the content of the site is strong and there are lots of high quality incoming links. Google Webmasters tools are a free way to get some good insight in to your domain. There are better tools out there, but Google Webmaster tools is a good first start.