It is important to keep your data around for a number of years (often specified in your project plan, funder requirements, or the law). Safely stored or archived data backs up your research and protects your scholarly reputation. You may also want to reuse the data later on.
Storing data involves arranging a secure solution using servers and/or devices, both during and after the data collection process. Sensitive data must be encrypted. Storage also involves some human consideration, too: who will be in charge of the stored data? Who will be trusted with access? How long should the data be stored, and who will securely delete it?
Archiving data entails more care: you will provide documentation, prepare the data for long-term storage, and straighten out institutional or organizational support. You may have to work out an archiving solution with your department or institution, or you may choose to submit the data to a trusted repository. The method of archiving your data may therefore also be how you share your data.
A repository is an online vault for materials contributed by many people. Depending on the repository, its contents can be publicly available, restricted to certain people, or embargoed (delayed for a number of months).
The below repositories accept data. You may have to apply to be able to contribute your materials. All contributions are credited to you and belong to you. Other repositories not listed may be built to accept articles only; others accept supplemental data bundled with the article.
Subject-specific data repositories:
How do researchers share their data?
Many scholars choose to make their research data available to the scholarly community or to the public by:
• • • • •
Why would researchers share their data?
* More impact — references:
Simple Open Data is a list of helpful hints to make sharing your data simple and effective.
Just because you've put your data in a repository or on a storage server, it doesn't mean your data will be useful in the future to those who want to use it. Without documentation and organization, future researchers who are looking at your data may be confused about its context or usage.
The core guiding principle is simple: Someone unfamiliar with your project should be able to look at your computer files and understand in detail what you did and why […] Most commonly, however, that “someone” is you. A few months from now, you may not remember what you were up to when you created a particular set of files, or you may not remember what conclusions you drew. You will either have to then spend time reconstructing your previous experiments or lose whatever insights you gained from those experiments.
(William Stafford Noble  A Quick Guide to Organizing Computational Biology Projects. PLoSComputBiol 5(7): e1000424. doi:10.1371/journal.pcbi.1000424. Emphasis mine.)
Read this short lesson, Preserving Your Research Data by James Baker, for good summary of general best practices. (It's also the source of the above quote.)
See the Metadata tab in this guide for more about formatting your data itself.
The Open Data Commons wants all research data to be open and accessible. They provide a guide to licensing your data to protect the data creators and to let users know what can and can't be done to/with the data.
The University of Minnesota has a great guide to citing data, whether you're using someone else's data or providing a citation for your own.
Our Guide to Faculty Scholarship Resources highlights other ways to track and measure your scholarly activities.