There are already several established international databases where you can find and search for existing research data. Among these there are databases that cover a big variety of research subjects and also databases that are more limited. Below you will find examples of both
Pangea is operated as an Open Access library aimed at archiving, publishing and distributing Earth & Environmental Science. Most of the data are freely available and can be used under terms of the license mentioned on the data set description.
Zenodo is a multi disiplinary, international database that contains all fields of research, all types of research artifacts as long as the content don't violate privacy or copyright, or breach confidentiality or non-disclosure agreements for data collected from human subjects.
Research data registries and search engines
Re3Data is a global registry of research data repositories that covers repositories from different academic disciplines.
DataCite gathers metadata and use it for a large index of research data that can be queried directly to find data, obtain stats and expolre connections.
Google Dataset Search Google's search engine to help researchers locate online data that are freely available for use. NB! Beta version!
Base (Bielefeld Academic Search Engine) is one of the world's most voluminous search engines especially for academic web resources.