Something like this is complicated and painful if not done right, but Qrank (or QRANK, if you want to shout about it) has it just about dead-on. The login process is kind of a pain, but once things are set up, the quizzes move fast, and the questions are an interesting mix of history, pop culture, and general knowledge. The constant updates are a huge bonus as well; with a lot of quiz games, questions tend to repeat themselves, but the flow of new information means that there are new questions to answer every day.
I'm not 100% sure of the business model; there are ads, and I had a few questions that seemed branded (they made explicit mention of actual products). That leads me to believe that there are probably a few ways that Ricochet Labs is making money from players, and not all of them are completely clear. That may not bother you, though. If you've got a few friends to match scores with every day, Qrank seems like a fun, daily diversion into trivialand. Technology is making social, quickly updated games like this one much easier, and I think we'll end up seeing quite a few more of these in the future.