I plan to visit Denmark for 5 days during holiday season here in the States. I'll require a Schengen visa to enter Denmark. When I was going though the checklist for the visa application, there is one entry that is not very clear. It says about an invitation from a Danish national or a person holding a PR card. I've visited the EU in the past but had the invitation from the organizer of the conference that I was going to attend. Does this mean that I can't apply for a Schengen visa to visit Denmark without knowing a Danish national?
If you are travelling for tourism or personal reasons, you need an invitation letter only if you are staying with a host. If you are staying at hotels, then an invitation letter is not necessary (use hotel bookings instead).
Regulation (EC) No 810/2009 Annex II contains the legal verbiage...
for journeys undertaken for the purposes of tourism or for private reasons: (a) documents relating to accommodation:
- an invitation from the host if staying with one,
- a document from the establishment providing accommodation or any other appropriate document indicating the accommodation envisaged;
If you need a visa, you can certainly apply for one without any invitation, e.g. if you intend to visit for tourism. In that case, you should submit other kind of evidence, like an itinerary.
I haven't seen the checklist to which you are referring and it might be clumsily formulated but invitations are only recommended when it makes sense with respect to the purpose of the trip (e.g. to visit friends or attend a conference).