Finland-Sweden. That's especially important in ice hockey, even if I personally think it's greater when Finland beats Canada. On the other hand, losing to Canada isn't that bad as losing to Sweden, you can say Canada is too good, but Sweden is a country Finland should be able to beat.
I don't know if most Americans consider any country a "rival" but I guess more and more people want to beat out China at the Olympics etc.
well, you can't build a proper rivalry when the most popular sports in the us are for the most part not popular anywhere else. there is some rivalry between the us and mexico when it gets to football (not the american version of it which is pretty much irrelevant everywhere else).
austria vs germany will be relavant once again tomorrow.