Take the Trending Now box from Yahoo.com: Ghostbusters 3 (don't care), Jwoww (I'm intrigued), Fox Stars in Danger (don't care), Zimmerman sues NBC (don't care), Norv Turner fired? (don't care), Brooke Burke cancer (don't care), LeAnn Rimes pills (don't care), Anchorman love interest (don't care) and NFL rule change (don't care). Of the top 9 things, I care about zero of them.
High level idea: I wish there was a way for me to filter out topics and all websites I went to would automatically remove things I have explicitly stated that I have no interest in. Hunny Boo Boo? Gone. Jersey Shore? Gone.
Possible solutions:
1) Browser extension: There might be something you install which knows how to filter the most popular sites of the internet. It wouldn't be perfect since site owners would be constantly changing their code and the extension builders would be in a never-ending catchup game.
2) Protocol level communication: It would be nice if the browser could send a blacklist of topics that the user wants to ignore and hopefully the site would implement a way to filter those out on their own system.
Why process of elimination instead of process of inclusion? If you just say what you like, the Internet becomes boring. We want to be exposed to new and interesting things that we didn't know we'd like.
Money: I don't know how to make money with this.