In the mid-nineties, when the web was new, people thought of browsing through sites as a lightweight pastime with little practical value. I'm sure this conversation happened a lot back then:
"What were you doing this afternoon?"
"Oh, I was just surfing the web, killing time."
Today, we use web sites for shopping, banking and doing serious productivity through web tools. You can "use" the web, "browse" the web or "navigate" to a website, but please don't say that you "surfed" the web.