You can share your data in many ways.
A data repository supports the preservation, discovery, use, reuse, and manipulation of data objects. A data repository often provides added value to data through quality assurance and metadata enhancement. Many data repositories are discipline-specific. The goal is to have a one-stop place for datasets concerning certain subjects, such as astrophysics or archeology.
ICPSR, at the University of Michigan, has one of the largest and oldest data repositories, which focuses on social sciences data.
You can also browse this list of disciplinary data repositories.
Many journals encourage researchers to submit supplemental data files so as to promote research transparency. As you consider where to publish, keep an eye open for journals which have this feature. Additionally, consider open access journals, so as to further increase the reach of your research. Learn more about Open Access.
Assuming your data has been fully prepared for sharing, one option is the share your dataset via Github. Github is a web-based hosting service based on the GIT version control system, generally used for software development. At first blush, one may not think it would prove to be a useful venue for open datasets. However, many of the same aspects which make Github attractive for collaborative software projects apply to data sharing as well.
First off, Github is free for open source projects. Secondly, and more importantly, is the aspect of version control. Version control allows you to easily add to and track changes to datasets. Github also allows other users to make copies of your data repository. These copies are now manipulatable independent of the original, but still linked by their histories.
The drawbacks to sharing via Github are:
However, sharing via Github may make sense:
For an in-depth guide to sharing your data via Github see here.