BOINC is possibly the largest, and most populated network for computing. As such it attracts the most and highest quality projects to its platform, most of which are scientific in nature. While some of the project descriptions baffle even me, (and I thought I had a decent scientific education), there are some projects that have a great allure. World Community grid is possibly the project that generates the most buzz, as every single project that runs through World Community Grid is aimed at helping the world. Sample sub-projects include: The Clean Energy Project, Computing for Sustainable Water, Help Conquer Cancer, which as their names suggest are aimed at improving our knowledge in these areas to better achieve these tasks. Other projects available at BOINC are aimed at other area's of science or mathematics, whether you wish to search for something, from Radio Pulsar's in our universe, to an undiscovered prime number. Or just crunch numbers on a conjecture whether its the famous 3x+1 conjecture ( Collatz conjecture), or try and find out if all trees really do have a Harmonious coloring (something that appeals to the graph theorist in me).
You may be wondering with the super computers, and high powered computing clusters out there, what good is your home computer at making any sort of sizable contribution to science. While on a direct comparison your computer likely can not compete with these others on a pure number crunching basis. But in terms of shear number of computers of each type, personal computers by far completely outnumber these super computers, or High Powered Computers out there, and when you can harness even extra/ wasted computing cycles in your personal computers there are many many floating point operations (FLOPS) going unused, that could have been put to use towards a task you would like to support.