If you take a course for no credit, you will be auditing the course. Most colleges and universities allow auditing under certain circumstances, and doing so may be a good idea as long as you're clear on the implications.
Why Audit?
You might audit if you don't have time to do all the work, the course isn't required, you believe it will be good for graduate school or professional life, or it just interests you.
Credit
Colleges and universities do not assign credits for auditing, but the course will show on your transcript as having been audited. If you quit attending, you may receive a "W" for withdrawal.
Permissions
Most schools require that you get the professor's permission to audit, which she may or may not grant based upon seats available and other considerations. Sometimes department approval is also necessary.
Work Load
Some professors will let you audit only if you agree to do all or some of the work, even though you won't receive a grade. You must clarify expectations when you get permission.
Status
Because audited courses don't count for credit, auditing may affect both your full-time enrollment status and financial-aid status, if you slip below the required number of credit-bearing courses.