I think I know the solution to the problem (for me anyway)!
I have been plagued by this CC problem for months. I even bought a new machine because of the stress it caused me, and not to mention the lost work hours!!!! But since buying the new machine and having it happen again, and again and again, which has lead me rule out all font, software, plugin conflicts, because there is nothing on my machine that was on the old one. All of my old files are on an external hard drive and I have had illustrator crash several times with the hard drive ejected. This is what leads me to think (in my case at least) that the machine/files/plugins are not the problem.
CC membership allows you to run the Adobe applications on 2 machines, in most people's cases that's home and office. I have two machines one for work with one set of preferences that my CC account was made with, and another machine at home that is a shared and has an entirely different set of preferences. When an Illustrator file is left open on my work machine with a long period of inactivity (e.g. over a weekend) illustrator on my home machine crashes constantly (as soon as I try to move an object it crashes). As soon as Illustrator is closed down on my work machine, Illustrator on my home machine is then fine! And then both machines will run Illustrator CC again simultaneously until the work machine is left for another long period of inactivity (a couple of days) then, when it is, my home machine crashes again.
I noticed that each time Illustrator asked me to send a crash report to Adobe, it would use the email from the preferences on my home machine, not the preferences on my work machine (which is the email that the CC account is registered with). It could be that leaving Illustrator CC open and inactive for a couple of days causes some kind of 'time out' period on the account.
This could explain why Illustrator CC would work again on my home machine (briefly) when trashing the preferences.
So to re-cap I have solved my seemingly inexplicable problem by making sure that Illustrator CC is not left open for long periods of inactivity (2 days seems to be the threshold) on one machine, if the account is being shared across two machines.
Please let me know if this A. makes sense and B. helps anyone.