It depends on the project, but in my experience many (if not most) people end up making their repos public.
As for finding them, I'll often just look up the hackers on GitHub and check if they have new repos.
Though that's not always the case. I kept the repo for the hack I made this weekend (http://socialsecurity.io — antivirus for Twitter) private because I'm commercializing some of the machine learning.
Most of the teams I talked to, mine included, were using private repos. As much as I trust the community and my peers, it would be interesting to require public git projects during a hackathon. Not only would they be a fantastic learning tool, the potential data visualizations would provide a really cool postmortem.
As for finding them, I'll often just look up the hackers on GitHub and check if they have new repos.
Though that's not always the case. I kept the repo for the hack I made this weekend (http://socialsecurity.io — antivirus for Twitter) private because I'm commercializing some of the machine learning.