Can you give an example of such tasks?
I'm particularly interested in tasks, relevant to quite large amount of people, which could be solved by using distributed computing. (Not a global projects, such as SETI@Home, Folding@Home, etc)
As example we can take rendering and http://www.renderfarm.fi community.
Cryptocurrencies mining is not relevant.
Thank you!

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2 Answers
Well, I don't know much about rendering, but when talking about tasks that can be solved by distributed computing, you will probably want to take a look on Bag-of-Tasks (BoT) applications.
"Bag-of-Tasks applications (those parallel applications whose tasks are independent) are both relevant and amendable for execution on computational grids. In fact, one can argue that Bag-of-Tasks applications are the applications most suited for grids, where communication can easily become a bottleneck for tightly-coupled parallel applications."
This was taken from a paper that talks exactly about Bag-of-Tasks applications with grid computing. You can read the full paper here.
Now finding a task relevant to users is a matter of creativity. This list of distributed computing projects might give you some insights.
Setting up the BOINC server and, mainly, programming the BOINC applications will be the hard tasks here. This BOINC wiki helps you to have a notion of what is needed on the "background" of a BOINC project.

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Old question, but fresh answer.
I have my own Distributed Computing Library written completely in C++ (search for gridman raspberry pi).
I am using it for: - Distributed Neural Networks training / validation - Distributed raytracing (for fun) - Distributed MD5 crunching (for fun) - Distributed WEP crunching (for fun) - Distributed WPA crunching (for fun)
And in general, i always think of it this way: If something takes too long time for me, then i split this into several PC's. Real world examples?
Take Investment Banking for example, all these models have to be calculated milion times with different parameters.
Take Neural Networks - a good example, learning takes ages (depends on data) - if you split this into 10 PC, your results are obtained 10 times faster.

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