What is the best grinder for Greek coffee?

I would never consider using my burr grinder for anything that fine. There are any number of blade-type grinders that can grind much finer -- they just take attention since you can heat the coffee you're grinding a lot (as with spices ground the same way) and release oils.

The other drawback to blade grinders is an inconsistent grind -- but just pass the ground coffee through a fine sieve and that should take out any too-large bits.

I don't know if this helps but supermarkets have grinders for coffee and they usually have a "turkish coffee" setting.

Specialty home "Turkish" and "Greek" hand coffee mills ARE burr grinders.

The big supermarket machines that do Koukouvagia's Greek coffee are burr grinders as well.  Also, she just might possibly maybe know something about the subject.

If your electric, burr "espresso grinder" is at all good, it should not have any problem grinding for an ibrik.  The finer you grind, the greater the tendency to clog up the burr.   

The solution... wait for it... is to clean it now and then.  Preferably by disassembling, or using something like Umex Grindz grinder cleaner; but even shooting a little bread through it will make a positive difference.  

Getting rid of the rancid oils which stick inside every burr grinder is going to make a huge positive difference in your coffee -- no matter how fine you grind and how you brew.      

With all due respect to Suzanne, a propellor grinder is about the worst possible way to make fine ground coffee -- because of the heat inevitably generated and the inconsistency of the grind.  A lot of folks, including me, say it's okay for coarse ground as for a "French press," or to do a medium grind for a not-very-revealing brewing method like a paper-filter, pour-over.  But your Xtreme java maven is likely to insist on a burr grinder for everything.

BDL