While Academia is designed to be a way to spread knowledge, there are some ways to control the privacy settings of your Academia Profile.
If you have made your analytics public, and would like to make them private again, click the checkbox next to "Make my Analytics public" box, which should be checked if your analytics are public.
We bookmark all papers that you download for you, so you can come back to them on the site. If you no longer want other your followers to see what papers you're downloading or bookmarking, you can change uncheck the box that says "Create a public bookmark when I download a paper."
You also are presented a number of options regarding how you interact with co-authors on your papers. Please feel free to adjust them as you see fit.