Have you tried to reset the preferences (lose down Illy and press Ctrl+Alt+Shift/Cmd+Option+Shift during startup (easy but irreversible), or Move the folder with Illy closed (more tedious but also more thorough and reversible))?
Running the Cleaner Tool between uninstalling and reinstalling clears all the mess that may linger after a simple reinstallation.
I have restarted yet again (second time after safe mode) and now AI seems to be working. So I think all is well for the moment.
Mylenium - Thank you for your reponse, I will make sure to include crash logs if I post another question.
Jacob Bugge - Thank you for your response, glad to know another thing to try if the problem returns. I did not realize that reinstalling does not automatically reset/clear everything.
I think I know the solution to the problem (for me anyway)!
I have been plagued by this CC problem for months with Illustrator, In Design and Photoshop. 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, I have ruled 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 CC 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. Here's what has worked for me, and where I think my problem stems from:
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 shared and has an entirely different set of preferences.
When an Illustrator file is left open on my work machine (the machine that the CC account was created on) with a long period of inactivity (e.g. over a weekend) Illustrator CC on my home machine crashes constantly (as soon as I try to move an object it crashes). As soon as Illustrator CC is closed down on my work machine, Illustrator CC on my home machine is then fine! And then both machines will the 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 also noticed that each time Illustrator CC asked me to send a crash report from my home machine to Adobe it would pull the email from the preferences on my home machine, not the email that the CC account was made with (which is the email on my work machine). It could be that leaving Illustrator CC/any of the CC apps 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 account 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.
Don't know if you've figured this out yet or not, but I also ran into this problem recently and I solved it by doing this (I have it installed on two machines)
1. Make sure both installations of Illustrator are up to date on both machines that it is installed on.
2. Turn off Typekit syncing in CC preferences. CC>Preferences>Fonts>Typekit On/Off
3. Uncheck "Preferences" under Sync Settings in Illustrator. Illustrator>Preferences>Sync Settings
4. Go to Finder>Library>Preferences. Delete the Adobe Illustrator Settings folder completely.
5. Restart computer.
This fixed the issue for me. However, I don't know if you're running your CC account on multiple machines. You could still try the above steps even if on only one machine and see if it helps.
I am having this issue as well. I have tried restarting, uninstalling all (not just illustrator) Adobe CC products, running the CS cleaner tool, and resetting my preferences on startup... Nothing is helping.
I'm on a 15" MacBook Pro (2014)
16 gigs Ram, 2.5 ghz i7, OSX Yosemite.
I will try restarting again. Please tell me I don't have to go back to my PC...
I am also having this problem since recently on my Macbook Air (Mid 2013) running OS X 10.9.5. I've tried all of the suggested solutions here and nothing is working. After running Adobe programs for 30 mins or so after restart, anytime I drag a file in Illustrator the program crashes. Same for Premiere Pro (except the crash only occurs sometimes in Premiere, but dragging becomes disabled).
I've exactly the same problem with illustrator cc and big issues with indesign cc (can't move any objects). i even formatted my hard disc and re-installed Yosemite… I really need some help, because i can't work with this probelm and there is some clients work waiting to get finished… …
Imac 27" end 2012
24GB 1600 Mhz DD3
GeForce GTX 660M 512 MB
Had this issue pop up expectedly several times and it's a real hassle to fix. I solved it last time by uninstalling Illustrator, trashing prefs and running the Adobe cleaner tool. The issue doesn't appear to be specific to a particular file as I can create a new document and reproduce the crash by creating a simple box object, then selecting and dragging it.
For whatever reason I can't upload the full crash log, the communities returns an error but basic OX/App version details are below.
Process: Adobe Illustrator 
Path: /Applications/Adobe Illustrator CC 2014/Adobe Illustrator.app/Contents/MacOS/Adobe Illustrator
Version: 18.1.1 (18.1.1)
Code Type: X86-64 (Native)
Parent Process: ??? 
Responsible: Adobe Illustrator 
User ID: 502
Date/Time: 2014-12-29 10:07:33.557 -0800
OS Version: Mac OS X 10.10.1 (14B25)
Report Version: 11
Anonymous UUID: C917C5D1-87A9-1045-865D-5E580501E8BC