There are several online repositories where you can store and/or make your data accessible online. Some are discipline-specific and accept only data, whereas others are not, like the examples given below
SMU Scholar is an institutional repository managed by Bepress. Users can submit different types of materials into designated collections for public open access. SMU Scholar provides a central location for all university research output and has a simple submission process. There is a 2 GB per file limit for items uploaded to SMU Scholar. Materials uploaded to SMU Scholar will be harvested into the university digital preservation system, Rosetta.
Box is a cloud storage and file hosting system. Users create boxes and folders containing items and manage permissions for these items. Currently the university contract with Box allows for unlimited storage space and Box allows users to take advantage of the cloud storage distributive model. There is a 15 GB file size limit which might be a hindrance if researchers want to keep files together in a large zip file.
Harvard Dataverse is an iteration of the Dataverse web application that Harvard has made open to outside institutions and researchers. Simply create an account and set up your own dataverse. Harvard Dataverse provides a full back-up of material stored in its system. There is a 2 GB per file limit for items uploaded to Harvard Dataverse.
Click here to see the Research Data Management Support policy.