I'm sure the Swiss do, but just an aside that plenty of EU countries allow members from other countries to vote in their elections. E.g. here in Ireland I think we only restrict constitutional referenda to Irish citizens.
It seems it does vary heavily by country [1]. My country (Romania) does not give any voting rights to foreigners (AFAIK), and I thought the US didn't either.
But, the US is a democracy by name. I'm not sure where you're coming from by saying it isn't.