Anyone planning residence in Germany for a continuous period of longer than
60 days must register with the local authority within a 7 days of taking up residence. Temporary residence does not require registration. Temporary residence under 60 days is typically people here as tourists or on short term trips, living in hotels or temporary accommodation (Note however, that some cities which charge a "Kurtax" - one local example being Bad Tölz, and require registration of anyone staying more than 24 hours and paying for their accommodation e.g. in a hotel). Control of registration is lax, especially for EU passport holders or for people travelling between countries under the Schengen agreement, but if you are "checked" on the streets you could be caught out, although this is pretty rare unless you attract attention to yourself. Children under 16 years old living with parents in the same residence do not need to register.
Registration is a simple formality, but does require that you are legally entitled to reside in Germany. ALL EU passport holders
who have proof of adequate income or financial support and with accepted insurance for health have this entitlement without any further action or paperwork. Non-EU require permits dependant on country of origin and reasons for residence. Age (over 16), employment status, etc., does not affect the requirement to register.
Proof of registration is required for many other activities, such as registering a car, claiming child or unemployment benefits and for some
health insurances. Failure to register can be penalised by a fine of up to €500 (per person)