To www or not to www, that is in the URL …
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Since people link for a variety of reasons (directory listings, forum posts, blogs), you can’t control how they will link. However, if you allow both www and non-www versions to exist, duplicate content will be created in the search engines. Creating 301 re-directs assures only the desired version will be in the address bar when the searcher arrives (typing the undesired one redirects the user to the desired version) and that only the desired version is indexed when those links are crawled.
So www or not?
3) Linking / Incoming Links (links from other sites):
Here, probably more so than anywhere else, the choice becomes clear. Incoming links are important for rank and to a large extent, the more ‘in-links’ you have the better. You may have noticed that when you start typing a URL with the www many editing programs will recognize you are typing a URL and create a link automatically. This auto-linking takes place in many places, including forums, blog posts, signatures, video captioning, and in press releases. Press releases are especially important as they are often picked up by other sites and republished providing a good source of relevant links to your site.
For a brief period I left the www off URLs in press releases, while the treatment of www varies, I found in many cases where the www had been included URLs were automatically linked, however when the www was left off, URLs were never linked.
Recommendation
While it may be visually cleaner to use mywebsite.com, I recommend that you always use www as your default domain and include the www in any electronic postings. A raft of programs/websites recognize the www as the start of a URL and will automatically link the text. While this may seem trivial, you want as many linked references to your site as possible and all those blog and forum postings, videos, press releases, et cetera add up!
How about Business Cards, etc…
Here I see having the www or not having the www as strictly an issue of preference and I would use what ever fits the space and looks the best.
There are places where it is desirable to use a shorter URL. The most common example would be Twitter. But remember, declaring www as the default domain won’t make the non-www version stop working, so you can always use the non-www in places where you need to keep things short.

If your seeking help with a Windows-based server (IIs), this is a good article on 301 redirects:
http://www.jlh-design.com/2006/08/301-redirects-in-asp-on-iis-server/