I have had the exact same problem since I upgraded to Yosemite. The latest upgrade (10.10.1) makes no difference: Safari stops loading any page for no good reason. Chrome and Firefox keep on working just fine. Checking back after a while - here is Safari working again. Why ? No clue.
The apparent solution is therefore to (again) ditch Safari and come back to Chrome. Besides the fact that I like to understand what happens, this is, alas, not enough, and the problem may lie elsewhere.
It happened to me again yesterday: I was working all morning using Safari. Then I step out for 1/2 hour to grab lunch. I come back, and - you guessed it - Safari is locked. Out comes Chrome which works just fine.
But then I noticed several things:
1) Calendar has a spinning wheel and eventually declares it is unable to reach any of the iCloud calendars (as well as my corporate calendar).
2) Same for contacts: it spins a while then declares it is unable to reach the iCloud contacts
3) App Store (I had an update pending) just hangs. Eventually it stops saying it can't connect to the app store
4) Mail: emails stop displaying any images. Presumably the image URLs in the <img> tags just 404.
But Chrome and Firefox work just fine.
My conclusion is that something blocks some network interactions, but only for Apple apps. The symptoms are different for different apps. Safari becomes a useless brick. Calendar and Contacts keep on working, but they no longer synchronize, ...
Others applications don't care: Chrome, Firefox keep working their merry way.
Maybe some network-related daemon crashed ? You would expect to find some clue in the system logs. Forget it: it is virtually impossible to find anything conclusive from those logs. My log has gazillions of messages hinting about myriads of obscure infos, warnings or failures. Good luck finding anything sifting through that mess. Log entries are not even properly tagged as fatal/error/warning/info like any proper logging system does.
At the end I had to reboot my MacBook (I hate that: it is so **** slow) and everything is back again.
That is until the next occasion it happens again. I could not care less having Safari dying. But losing calendar and contacts synchronization is a pain and so is losing images from Mail.