Unless searching for online docs, looking up error codes and error messages, etc., I do relatively little web search and browsing anymore - compared to even a year ago. I usually rely on good links from Twitter and Google+ to find things worth reading, keep up with new tech, and sometimes even read the news.
In the 1980s, I was a "find useful stuff at public FTP sites" resource at SAIC. I spent time maintaining lists of useful FTP sites and what they contained so I could help people quickly find stuff. Gopher was a step up. Good search engines were a huge improvement for finding stuff on the web.
Now I find myself mostly depending on what interesting people recommend. Even though I am a techie and don't represent a typical Web user, I still think that the trend of using social media to find interesting (and even useful!) material is widespread. It will be interesting to see how the major web companies like Google, Amazon, Microsoft, Yahoo, etc. perform financially in the future because it seems very difficult to predict new disruptive technologies that will capture peoples attention and interest.