I'm an EU citizen (non-Swedish) who currently lives in Sweden. I'd like to host my friend (US citizen) who wants to visit me in Sweden. So what are the requirements that I should fulfill? My friend isn't required to get a visa to enter Sweden. Would my friend be asked to show proof of financial subsistence at the airport?
You do not need to do anything. Your US citizen friend can enter the Schengen area for up to 90 days without a visa. If the border officer asks your friend what their plans are, then "visiting a friend in Sweden" would be an entirely normal answer and should not pose a problem.
There is always a small possibility that your friend might be denied entry to the Schengen area upon arrival, but there is nothing you can do that would influence that one way or the other.
The actual requirements are (from Wikipedia):
To be able to enter the Schengen Area/Bulgaria/Croatia/Cyprus/Romania visa waiver, the above Annex II nationals are required to:
- have a travel document which is valid for at least 3 months after the intended date of departure and which has been issued in the previous 10 years
- have a machine-readable passport with digital photo or a biometric passport
- have sufficient funds for their stay and onward/return journey
- justify the purpose and conditions of their stay
- not be listed in the Schengen Information System as someone to be refused entry and not be considered as a threat to public policy, internal security, public health or the international relations of any Schengen country.
There is a requirement for "sufficient funds", but in my experience a well-presented traveller won't even get asked about that.