One good writing activity is to write a letter to your future self, past self or to someone you know that you don't intend on sending. Another good activity is to write about an argument two characters are having. Write from one perspective; then, switch and write from the other.
Free writing, also known as flow of consciousness or train of thought writing, is an activity in which the writer simply writes from the top of his head. This activity is often taught in college, and the idea is to write without stopping to think or edit. The intended purpose is to link writing with the subconscious and non-judgemental mind.