I too have had more than a year of weekly system freezes that only occured when Safari was running. My screen would actually freeze so that only mouse movement but no interaction remained. Nothing in the logs tipped me off. I cleared prefrences, plug-ins, and tried a dozen typical troubleshooting steps to no avail. I finally noticed that Safari was the only common factor. When I stopped using Safari a few months ago reliability went to 100%. Still hoping I can track down the root cause one day. Maybe Safari leverages the graphics card and my graphics card has a fault? Wild speculation is all I have.
I have this exact same problem. If I don't use Safari, my Mac is 100% rock solid - it never crashes. If I do use Safari, I can guarantee that the UI will crash after a while so that the only interaction I have with the computer is through the mouse, which can be moved around the screen but clicking has no effect.
Note that in most respects the computer is still running - I use Radium to listen to internet radio and this will continue playing. This shows that the operating system is still pretty much running fine, certainly all the parts of it that govern connections to the internet and playing sound.
I have had this problem for quite a few years now and so have had to switch to using Firefox for web browsing, which is not exactly a big hardship, but I do wish I were able to use Safari as it just is snappier with a number of websites.
My Mac is a late 2009 iMac 27 (ATI Radeon HD4850) running Mavericks 10.9.2 with 16GB RAM. I have often wondered if this is a graphics issue, maybe with the drivers, but since there is never any indication in any log of the problem I cannot pin it down in any way. I keep hoping that a system update will fix the problem but it never has yet.
Interestingly enough my computer is exactly the same as yours albeit with only 8G memory and I also suffer from the Safari UI crashes with just the same symptoms. I get it maybe once every 2 or 3 days and I believe primarily when I'm scrolling with the Magic Mouse but not sure on that.
One time I tried going into the frozen machine with screen sharing from another computer and that actually worked - I could get to the desktop.
There was some discussion that the problem was with Flash but I updated to the latest and no difference.
One of my other computers is a newer 27" iMac of about the same configuration and that has no problems at all. Go figure.
To me it's basically an irritaion and can be lived with. I also can't see any issues from having to power down and restart.
Hopefully 10.10 will fix it, I'm just hanging on.
Agree it is an irritation, and in my case it is alleviated by not using Safari.
My Mac is normally running for upwards of 40 or 50 days between restarts - basically I only ever restart when I have to and just put it to sleep at other times. That way I can have all the documents that I am working on open in all the different applications (primarily Word, Excel, Illustrator and Mail) and skip backwards and forwards between them all as appropriate. So being forced to restart by Safarir crashing the UI is not tolerable for me!