The vaccines produced by BioNTech/Pfizer, Moderna, AstraZeneca, Johnson & Johnson and Novovax are currently approved in Germany and the European Union.
Versions of EU-approved vaccines that have been approved abroad (original or licensed production) are also recognised. A list of all approved vaccines for people from countries outside the EU can be found here: https://www.pei.de/SharedDocs/Downloads/EN/newsroom-en/dossiers/namen-covid-19-impfstoffe-ausland-en.html;jsessionid=C1C357E151414E675481EB6A7A989ECE.intranet221?nn=164146
People who have been vaccinated with vaccines not approved in the EU are subject to the same rules as unvaccinated people in Germany. You must have a valid PCR test or antigen test (up to 48 hours) prior to travel, depending on your country of origin. It is important to inform yourself of the travel regulations and requirements applicable to the respective country for travel to Germany and Europe. Information is available via the German embassy websites in the respective country or via the embassy of the respective country in Germany.