Moving to EU, do I need a return ticket? [closed]

No, a return ticket is not required, but other restrictions may apply.

For a tourist or temporary visitor, without a return ticket, border guards will doubt if you actually plan to leave the Schengen area after your authorized stay and can refuse entry if they are not satisfied that your plan is genuine.

No visa is required

But this does not apply when your spouse travels with an explicit purpose to move to Germany with you for a long-term residence. American citizens are entitled to apply for a long-term residence permit after entry without visa in Germany.

Citizens of the United States of America, Australia, Canada, Israel, Japan, New Zealand, Switzerland, the Republic of Korea, as well as EU citizens may apply for their residence permit after entering Germany without a visa.

https://www.germany.info/us-en/service/visa/family-reunion/922294

Some airlines may insist to check (erroneously, but happened to me twice) for a return ticket for non-visa nationals, but your marriage certificate should be sufficient.

But Germany imposes other conditions

As you are a German citizen, unless you can otherwise derive EU rights from previous residence in an EU country⁽¹⁾, the German law applies and your wife is not entitled to claim EU free movement rights. That means she must follow German law and requirements to obtain a residence permit.

Among others, she must demonstrate knowledge of the German language at A1 level.

Usually this is checked by the local residents' registration office when submitting an application for residence permit, not at the border.

Covid-related restrictions

Due to the pandemic, other restrictions may apply:

Generally, nationals of countries outside of the EU who are members of the immediate family (spouses, children under 18, parents of children under 18) are permitted to enter Germany for the purpose of joining their families if the necessary requirements for entry are met (e.g. D visa). The family members are allowed to enter Germany for reunification with the reference person or together with the reference person if the reference person is entering Germany for the first time for the purpose of a long-term stay. However, the reference person must be exempted from applicable entry restrictions.

Entry for the purpose of marriage is also possible.

Short-term entry by immediate family members who are citizens of countries outside of the EU

[...]

Spouses or civil partners of citizens of Germany, of another EU country, or of Iceland, Liechtenstein, Norway or Switzerland are allowed to enter Germany regardless of whether the reference person has his/her permanent residence in Germany or abroad. In these cases an urgent family reason is no longer required for entry. This is the case regardless of the whether the reference person additionally holds the nationality of a country outside of the EU.

The following documents may serve as evidence that one is an immediate family member (depending on the type of family relationship):

• marriage certificate, certificate of civil partnership;
• birth certificate;
• notarised extract from the family record or the civil status register.

If the traveller is entitled to enter Germany without requiring a visa, the authenticity of official foreign documents must be verified unless the documents were issued in one of the countries listed in section 14 (1) of the Ordinance Governing Residence (Aufenthaltsverordnung, AufenthV) (Australia, Israel, Japan, Canada, Korea, New Zealand, United States of America).

(1) If you resided in another EU (incl. EEA and Switzerland) state for three months or more, and subsequently you did not live in a non-EU country for six months or more, your spouse are entitled to free movement rights under EU law. In that case, she does not to demonstrate any language skills.