This is an old question, and the two answers by the OP and @JakobChristensen do answer the question. I'll just mention that I'm finding the situation fairly confusing.
I recently (manually, not via NuGet) downloaded the current NuGet version, which they currently call "2.2.0".
https://www.nuget.org/packages/Microsoft.Exchange.WebServices/
But the internal file/product version on the .dll is 15.00.0913.015.
According to this page
https://msdn.microsoft.com/en-us/library/office/dn528373(v=exchg.150).aspx
the file should be placed here:
C:\Program Files\Microsoft\Exchange\Web Services\2.0\
So that's where I placed it. Later, when playing around with a Microsoft sample program I noted that it did indeed reference the file at that location.
But another Microsoft sample program referenced the file in the GAC!
C:\WINDOWS\assembly\GAC_MSIL\Microsoft.Exchange.WebServices\15.0.0.0__31bf3856ad364e35\Microsoft.Exchange.WebServices.dll
This version had file/product version 15.00.0847.030.
I'm not sure how that file got there, probably part of a Visual Studio installation.
There's also something called EWSCore, which is apparently a forked version of the official EWS with some bug fixes.
https://www.nuget.org/packages/EWSCore/
My current decision is that I'll consider the official NuGet version to be the version I'll standardize on, and manually download it to my development PC and my build PC and place it here:
C:\Program Files\Microsoft\Exchange\Web Services\2.0\