Generally speaking, for EU nationals, the EU freedom of movement applies.
Privileged nationals such as US-Americans, Canadians etc. can enter Germany and can apply for a residence permit locally in Germany (even though it is not recommendable due to long lead times at the immigration authorities).
There are further exceptions to the visa requirement, also e.g. for South American or Asian nationals. However, the requirement depends on individual conditions, e.g. (the entry as a dependent or the presence of a biometric passport etc.).