I would like to know if there are any statistics on turnover of Bitcoins for each country in the world. A very rough way would be to get a statistic on which traffic to Bitcoin.org by country.
Serith provides a link that shows location of Bitcoin nodes. Beyond that Bitcoin specifically makes geolocation stats difficult. Addresses are intentionally random and arbitrary. You can look at transaction to determine senders IP address however that can be obfuscated and will not correctly reflect anyone using a web based wallets.
For bitcoin generation that is more difficult as roughly 80% of all Bitcoins are generated via a pool so any data in blockchain will simply indicate the location of the pool not the miners that make it up.
You can see how many times bitcoin was downloaded by going to sourceforge and looking up bitcoin.
For example here is how many times bitcoin v4.0 was download by the United States:
Here is a breakdown of Bitcoin by countries taken form Google Trends:
What you can see in that Estonia and Finland are first and only after that comes the US.
I don't know how accurate it is, but here's a cool live map showing transactions - http://fiatleak.com. Portrays China having the bulk of the transactions, at least currently.
For a very rough guide you could look at transaction volumes on the exchanges for different currencies..