Haverford offers unlimited, cloud-based storage using Box, a content management platform. Box offers synchronization apps and collaboration features. It is also HIPAA-compliant. Box is an excellent option for storing data that you wish to keep private or share only with a small set of colleagues.
If you have data you'd like to share with the broader scholarly community, a number of free repositories exist. Some of these are subject-specific, while a few are domain neutral. The ability to assign metadata to your data vary widely across these platforms, a factor to consider if discovery of your data is of particular importance to you.