The UK had 113 Typhoons in 2013 and Germany had 112. When they're all delivered, the UK will have 160 and Germany 140. France has 95 Rafales and will eventually have 180. Sweden is not NATO, but has around 130 Gripens. Norway and Denmark have around 90 F16s between them, though you probably wouldn't call them modern. Not sure what the US has deployed in Europe.
Edit: not really modern, but Belgium, the Netherlands and Poland have another 150 F16s between them. Poland also has 30 or so MIG 29s.