The issue is caused by the file that is supposed to make the prediction of your autocomplete better. Go to $UserBaseDirectory/.Mathematica/SystemFiles/FrontEnd/SystemResources/FunctionalFrequency and check the .m-file there. Everytime this happens to me, this file was several hundred MB large. Deleting it solves the problem.

Though I do not know if this is a known bug (and I am on a Mac), you can bypass the autocompletion by going to the Preferences pane (from the Mathematica menu) and on the "Interface" tab uncheck "Enable autocompletion with a popup delay of xxx seconds". You can still bring up the autocompletion popup by typing command-k on the mac or (I think) alt-k on Windows. You can also leave the checkbox checked but change the default number of seconds for the popup to appear from the default of 0 seconds to a larger number.

Tom: I just reported a bug of this kind and sent the file (407mb) to tech support.

No problem, it happens quite frequently to me. A shame as well, since autocompletion without this file favors some weird suggestions sometimes (like when you type Integ... it will suggest "Integer" rather than "Integrate").

I keep getting the same issue as the OP. I've tried all of the above and it still freezes upon auto-completing even after I've increased the time and write simple functions as Plot, Solve, Factor etc. which takes less time to type than the auto-completing threshold I've entered.

Thanks for the tip David. I had thought of delving into the preferences to see whether I could turn autocompletion off, but it's a feature I rather like! In any case, after multiple crashes, Mathematica 10's kernel decided it had licensing 'issues' and I think had become corrupted. I had to uninstall it. I hope a speedy bugfix for Windows users is forthcoming, but for now, I'm back to version 9.1.