America doesn’t have any currently, but they may come.
I hear that Canada has them – a fixed annual charge of something like $100. Is that just for IFR, or VFR as well, and what are the weight thresholds, if any?
Eurocontrol covers a larger area than just Europe. I recall that they even collect the IFR route charges on behalf of Egypt!
NavCanada hits you with a charge for providing IFR nav services even if below 2t.I had to pay when transiting via Goose Bay enroute Greenland.
It was pretty expensive in the Mirage – Total of about C$180.
In Canada, only movement based charges apply for aircraft over 3 metric tons.
For aircraft weighing less, a small annual or quarterly fee applies.
See http://www.navcanada.ca/EN/media/Publications/Customer-Guide-Charges-EN.pdf
They charged me for North Atlantic navigation.
Have you tried the calculator on the website?
If you have been charged for something not chargeable you should appeal.