The loyalty programmes market in the USA is far and away a larger affair than Europe. Whilst I think Europe can catch up eventually, it'll take a few years still. A quick tip for people to take advantage of USA-based promotions is to get a forwarding address. This tip actually works whichever way round you like: having a European address and getting a USA address, or being a USA resident getting a European address. Heck you can even sign up for an Australian address.
You can sign up for a forwarding address at Shipito for $8.50USD and they will provide you with an address in California. Then just change the account of your loyalty programme to your new Shipito address before you register for your promotion. Just make sure you aren't signed up for any mailing promotions or Shipito will charge you for forwarding it to you!
I should say that if you have a friend or relative who has an address at your target location, you should use that as a first port of call.
The most notable promotions I come across which require specific residences are American Airlines' double EQM promotions where you have to be a resident of certain states – usually Texas, Illinois or California. You will also find that most USA-based airlines' online shopping portals require a USA address too. So from using my trick I have signed up for AAdvantage's portal and their dining programme.
Hope this page has helped. Short but sweet!