I'm experiencing the same with my Mac Mini (Model MC815LL) as well.
Originally, apps would just freeze (spinning pinwheel of death) including Finder so I tried booting to safe mode and repaired directories which seemed to work ok for a few days but now it's still freezing up.
Also when running more intensive apps like Netflix, I can get like maybe 10~15 minutes of video before the entire system crashes (frozen screen, noise for sound) and forces me to do a reboot.
Before that crash happened, I checked and saw that I was only using 10% of the HD (500 GB hard drive, only 50 GB used), plenty of RAM (8 GB in a 2x4GB configuration).
I'm now considering doing a clean install of Maverick to see if that won't help. But any other tips, I would really appreciate.