DeepL is a translator service that stands out for its very good translation quality. It doesn't support as many languages as Google Translate, but new ones are added all the time and there are already so many that it's unlikely to reach its limits.
European machine translation services
A machine translation service (translator) is a service that programmatically translates text from one language to another.
This category contains services from companies based in a member state of the European Union (EU), the European Economic Area (EEA) and the European Free Trade Association (EFTA).
You can read more about the listing criteria here.
European services
Reverso is a machine translation service from France. In addition, Reverso offers a grammar checker and tools to find synonyms and conjugate words.
ModernMT is a translation service from Italy, which improves from corrections and adapts to the context of the whole document and not just the last sentence. The parent company Translated (also based in Italy) offers human reviewed translation and access to the machine translation API too.
Textshuttle is a Swiss translation service. They can translate simple text input, editable files, and PDFs and offer translation solutions for businesses.
eTranslation is a machine translation service provided by the European Commission. It is free to use for public administrations, universities and small and medium-sized companies based in the EU. It can only be accessed after a registration.