A quick note on Academia.edu and ResearchGate
Two options that are often presented to scholarly authors to distribute your works openly are Academia.edu and ResearchGate. It's important to remember that unlike open access repositories, both of these are commercial enterprises (despite the former's top-level domain). That means they're in the business of selling things, including your user data. Please be cautious with utilizing such systems, and consider using open access repositories instead!
For a quick but thorough run-down of the issue, check out this post from Erzsébet Tóth-Czifra, and this broader guide to choosing and using academic sharing and networking platforms for Cornell's Gail Steinhart.
Open Access Repostitories
Depositing your work in an open access repository is another way to share your research. Be careful to comply with copyright and licensing restrictions when uploading your published work (see the "Know your Copyrights" tab in this guide). Repositories may be institutional, like Cornell's eCommons, or discipline-specific.
Publisher Copyright Policies
What happens to my copyrights for my own published work? Every publisher has different policies in regards to self-archiving and your subsequent use of your published work. The SHERPA/RoMEO database provides a searchable collection of publisher policies--check here when deciding where to publish.
Open Access Books and Textbooks
Data sharing is increasingly important in research and now often mandated by funding agencies. There are many discpline-specific data repositories, many of which are open access. Here are some resources for finding open access repositories in which to deposit your datasets: