What conditions need to be fulfilled to enter the Schengen zone visa free?

I'm aware of the canonical questions that answer most Schengen visa questions as well as numerous questions that ask about the 90/180 day rule. However, there is one case which isn't covered there: visa free entry. I'm hoping that we can construct a canonical answer about visa free entry. More specifically:

• Which countries/passports are permitted to enter the Schengen zone without a visa? Which authoritative sources can I check for possible policy change with regards to entry requirements for my given passport?
• Does the 90/180 rule apply to all non-EU/non-EEA/non-Swiss/non-Schengen microstate passports?
• What are the passport validity requirements for non-EU/non-EEA/non-Swiss/non-Schengen microstate passport holders wishing to enter visa free (apart from any airline requirements)?
• Are there any circumstances in which a passport holder from a visa free country would not be eligible to enter the Schengen zone? (e.g. International transit while not having any days available under the 90/180 rule, previous criminal/arrest records, bans by a member state, etc.)