I've recently gone down this path for one page sites, and responsive. The issue in the past was poor SEO, as Ray notes. However, my research indicates that if "sections" are used and h1 in each section, SEO is OK. A colleague ran some extensive testing on this theory and he was satisfied.
I have a couple of sites in play using one page set ups. I haven't tried the parallax effect yet due to viewing on smart phones, but I do have scrolling to sections on some of them.
Not all of these are live yet, but you can check out some attempts if you are interested.
http://ddhdesign.com/2014NEWBASE.php (not live yet)
http://smart-candy-shopper.com/index.php (top page only, then leads into PowerStore)
http://michaelstadler.com (jumps not scrolls)
using php/mysql for content on pages...