Generally every frequent flyer program has different offers for different countries stated in their profile, and as long as you don't expect a card to arrive in the mail (disable statements being set to you (which can often result in some extra bonus miles)).
Some programs require less mileage to reach a status level if your profile isn't set to the country in which this airlines has it's hubs. (because you supposedly have to go out of your way to fly with them).
Some time based offers will be sent according to your profiles country, but if someone forward you the the offers which often includes a link to register it will usually still work.
There are sometimes fixed differences between mileage required if your profile is set to a different country, than you will have to change before your booking the profiles country.
Note: Some programs although they let you change every day your profile, they will only adapt your first change for promos and other regulations (basically, only the actual mailing address will change).
If you have a specific program in mind, maybe state it here, and someone might be able to help you.