I have already used GeoIP (free database) with Nginx and it works.
I used the database GeoIP.dat that came installed with my Ubuntu server, downloaded the GeoLiteCity.dat file from MaxMind, added the variables in fastcgi_params and modified the nginx.conf file.

Now that I am installing a new LEMP server I have this question: Which GeoIP.dat file to use? The one that comes with Ubuntu 12.04 LTS (size 1.6 MB, date Jan 3, 2012) or a newly downloaded file from MaxMind (size 768 kB, date Jan 2, 2013)? Normally I would use the most recent one, but that one is half the size. Size isn't everything, but still ...