Sometimes I feel it takes a lot of effort to find questions I am interested in reading. I would love to be able to stumble solely on stack overflow. I would hit a button and it would bring me to a question that has been up voted by people that have up voted other questions that I have also up voted. I would also like to be able to configure the button slightly, allowing me to only go to questions with certain tags or ones that have no up voted answers. I know people will say you can already do searches and ignore tags but that often seems like a lot of work. Being able to come to stack overflow, hit stumble, and be learning or answering questions would really improve my experience.
Stack Overflow already has this, only better. When I go here it takes me to a whole page of unanswered questions that are interesting to me, instead of just one question at a time. I can click the "next" button at the bottom to be taken to a page with all new questions. ;)
This would be great functionality, especially since it cannot be done through the API (voting records are not exposed per user).
However, very similar functionality can be obtained simply by trolling your tags pages. Start with the questions that share tags which you have ranked on your user page (ie, tags with questions you've participated in).
This could also be automated by an enterprising stack app creator.
I disagree with Bill that the current unanswered page serves this goal, since it doesn't filter out questions that you are likely interested in.
Perhaps someone can make a StumbleUpon StackApp for this. But I don't know if they would have access to your upvotes (given & received), so they could recommend questions you are likely to find interesting.