Seventeen or Bust is a distributed computing project to prove the Sierpinski Conjecture. When the project started, there were 17 candidate Sierpinski numbers left to challenge the conjecture; the project sets out to find a number n for each of these k values so that k.2n+1 is prime. If primes are found for all seventeen candidates, the theorem will be proven; if the conjecture is actually wrong, the search will go on forever, hence the name 'Seventeen or Bust'.
So far the project has found 10 out of the 17 primes. It has a standalone app that runs on 1-8 cores with ease. We have the #4 team in the world and with a decent boost in crunching could potentially take #3.
Chess960@home uses Boinc and literally plays chess against humans or other computers in different tournaments or settings. You get small 5-6 minute WU's that are due within a few hours. It doesn't run 24/7. Our team is 8th, with several teams hot on our trail. I personally just run chess960 in addition to whatever else I'm doing since it doesn't always have WU's. When some become available, Boinc snatches them up and crunches them.
Anyways, it might not cure cancer or whatever, but both projects have real world results.