An overview of the many institutional and subject-based open access repositories is provided by e.g. OpenDOAR or re3data.org. There you can also search by country. Webometrics also provides links via repository rankings.
Members of institutions that do not have their own repository can use what are known as "orphan repositories". The orphan repository for EU projects is OpenAIRE, which also gathers data from other repositories. Für other projects, see e.g. OpenDepot.