I by no means started crunching projects expecting to get any sort of reward out of it other than knowing that I helped progress science. But lately I have found I have gravitated towards projects that offer some sort of reward, even if it is a measly graphic "badge" recognizing some level of accomplishment in the crunching. I do not know why but its nice to feel like you are getting recognized even with relatively little effort from the people running the project. A step up, is GPU grid offers two types of badges, level badges, which are based solely on credit towards the project, and publication badges, something that appeals to the academic in me, as these badges link to a specific scientific publication, and let you know how much you helped contribute to the science in that publication.
Possibly the most substantial reward I have yet to come across directly to the owners of the machines crunching the projects is done by Einstein at home. If you are the discoverer of a new pulsar you get rewarded with a nice framed certificate. For example a picture they shared from the last batch they sent out is here.
So I actually encourage projects to find some way you can quantify and reward their participants, even if it is in some completely small way. Also in my personal opinion the more you can tie it to success in a project the better. Currently the only badge I have is one for Harmonious Trees under Yoyo@home which appeals to the graph theorist in me, and I actually know some recent Ph'D students whose dissertation is in a closely related area of graph theory. Instead of just giving me a badge based on the number of credits crunched, it would be nice if they could "estimate" how many trees I found a Harmonious coloring for. Granted based on the projects this can get quite hard as I understand for some topics it may split that one task into many many projects to send out to the participants.