In WWW or Non-WWW, That is the Question on Industrial Search Engine Marketing, the question is asked: Is http://www.mysite.com better than http://mysite.com? – and there’s a good discussion which you might like to read.
But there’s a more fundamental question which everyone should ask, right now: does my own website work for the alternative way of typing in the address? For most of us, that means, if the “www.” is missed off, does it work? It ought to, because many, many people now just bash the last part of a website address into their browsers (e.g “bmon.co.uk“) without the “http://” or the “www.” and you don’t want them to think you’re no longer around. It’s a two-minute job to fix this and it shouldn’t cost you anything because any decent website manager should have had this working from the start.