(Note: this is a follow-up of the Minds business model discussion. A small explanation of - probably - the most successful reputation system on the web)
What I like more are similar business models that use reputation systems without the option to exchange to money. My favourite system is that of StackOverflow (SO). It uses points and gamification in a professional way (so it’s not a colorful game) to get users to maintain the website. This works incredibly well.
In SO you get reputation points by helping other users answer their software programming related questions. If your question and answer are good you receive points by the upvotes given by other users. You can also earn points by maintaining the sites (via moderation, editing posts, flagging, reviewing, etc.), plus you receive gold, silver and bronze medals (e.g. when giving N number of upvotes, posting M number of answers, etc.)
The only incentive, the benefit, to participation is, well… Reputation. Having a high score and many medals shows others you are an expert programmer, able to help and teach others. And this reputation also does well when applying for a new job and you show it to your potential future employer.
Software companies can lessen the burden on their support desk by pointing users to tagged Q & A on SO. The SO organization earns money by targeted ads (which are relevant to SO users, based on their interaction), and by having professional extensions for teams and enterpise organizations.
Also they run a whole bunch of other sites for different interest groups, that run the same software.