The European Commission states that EU citizens have the right to reside on the territory of another country "for up to three months without any conditions other than the requirement to hold a valid identity card or passport". Importantly, there is no requirement to register with the local authorities for a residence permit.
Unfortunately, it is not stated how you would count the period of three months or in another words when it would reset. For non-EU residents' Schengen visa, the '90 days in any given 180 days' rule is clear. However, I'm not finding any such rule for the 90-day maximum that applies to EU citizens.
A few examples: - Can a EU citizen alternate between two countries indefinitely with no conditions (e.g. stay in Schengen country A for 90 days, then 90 days in Schengen country B, rinse and repeat)? - Can a EU citizen stay 90 days in Schengen country A, move to Schengen country B for a weekend trip, then stay in Schengen country A again? How often could they do that in a given year?