Self-plagiarism is possible and it's just as serious.
Self-plagiarism, or "double-dipping," is deception and goes against the core principles of ethical writing. Papers are assigned for you to demonstrate what you have learned in a particular class. If you reuse a paper you wrote for a previous class, you are not demonstrating new learning.
Examples of self-plagiarism:
Ten Types of Unoriginal Work:
Source: TurnItIn.
Why do we reference other's work? Read Why Reference? in the Complete Guide to Referencing and Avoiding Plagiarism (2010).