As far as I can tell, a combination of different loan programs the government will loan any amount of money toward the cost of college with the only "limit" being for undergraduates. Your parents have to take out the loan for an amount in excess of the $12.5k to $18k yearly undergraduate limit. Once you get to grad school you can borrow the entire amount directly. Once you get to the Plus loan program (which doesn't appear to have any limit) there is a credit check required.
There used to be a private loan program (FFEL) where the government would guarantee the loan amount, but I think that was shut down in 2010. I'm sure you can also go to a bank and just get a loan directly, but I don't know what type of special rules apply to those.