Yes, loans can be used to cover living expenses. Schools will have a living expenses budget as part of the cost of attendance. For example, Michigan's tuition is $41,950. Living expenses are $15,000 (although this can be increased for health care costs). The total cost of attendance is $56,950. The total amount of scholarships/grants + loans cannot exceed this amount.
You can take out a total of $20,500 of stafford loans (federal govt loans, subsidized and unsubsidized). For the rest, it seems that most students these days are now opting for federal GradPLUS loans instead of private loans (where the credit requirements are more stringent) These loans are unsubsidized and carry a higher interest rate than the stafford loans, but you are permitted to take out enough loans to cover the cost of attendance. Depending on what state you live in/go to school in, there may also be state loan programs to cover the remaining gap.