Im guessing certain clearance levels would require background checks on family members as well??

Very much so. Not even just family members, although they might not conduct full background checks. They'll talk to current and former neighbors, supervisors, co-workers and classmates, and anyone you use as a character reference. And since they want to know that what they're telling them is accurate, they'll probably pull things like criminal records on them (oh, and they also talk to law enforcement anywhere you've lived, worked, or gone to school).

Oh, and depending on the level of clearance, you (and therefore, to a degree, anyone you associate with) get reinvestigated every 5 (Top Secret), 10 (Secret), or 15 (Confidential) years.

(Also, fun fact: Standard Form 86, the questionnaire for security clearance investigation, is 136 pages long.)