If you need a quick starting point for a new website, Templated is a place that has got you covered.
At the time of writing there are over 800 free fully responsive HTML5/CSS templates to choose from, so there should be something there that suits your needs. There are also premium plans available that gain you access to more fully featured templates.
You can use these templates for both personal and commercial projects, but you do need to provide a visible credit/link to the author somewhere on the site.
Why not check out the full template collection at templated.co