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Figshare is a public repository licensed under Creative Commons. It provides users a venue for making "all of their research outputs available in a citable, shareable and discoverable manner." Figshare even encourages depositing negative data.
Publishers are using Figshare for preserving their supplemental material, including datasets, e.g. American Chemical Society.
Harvard developed the open source software for Dataverse. It accepts data from anywhere and any subject. Other institutions worldwide have implemented Dataverse and initiated their own repositories which may or my not be open.
Zenodo was developed by CERN for OpenAIRE. Zenodo accepts research outputs from all subject areas - it is not restricted to the sciences. GitHub users can easily preserve their their repositories.
You can create a website for your research output. The UTARP project is a good example. All the data is in a repository freely accessible through the interface. You will have to make plans for the future maintenance and expense of running the website.