One of the trends these days is to lose the www. from your domain name.
Arguments for are usability (e.g. you don't have as much typing to do - it is easier to not have to say dubyadubyadubya every time you give out your web address).
There are counter arguments of course to do with cookie control and sites that have sub-domains etc.
What is important though is that you choose one and stick to it. In any event you should decide for one and not allow both.
Supporting both will cause duplicate content in Google and you may suffer in SEO terms.