In Denmark for instance JustEat and Trendsales were pretty successful. Both have a heave part of logistics involved though.
If you are making something digital then always think of your home market as a market of 6Billion people.
Successful startups out of Denmark 100% digital but none of them choose to stay there.
Tommy Ahlers Zyb (aquired by vodafone) and Podio (acquired by citrix). TrustPilot.com, Zendesk (moved to the US), Unity (moved to the US)
I agree that you should look at the world as your home market, but in practice there's more to it than that. Just opening shop in another country usually means incorporating for example. Our founder has mentioned a few times that his biggest regret was setting up shop in England after Sweden, instead of going after the US directly. In hindsight, the gain/pain ratio would've been a lot better.
It seems to me that the large home market is probably the biggest advantage US startups have (together with comparatively easy capital and a healthier attitude towards new ventures).