Government loans are credit independent. Subsidized loans are need based (the interest that accrues while in school is subsidized by the government), but unsubsidized loans are not. The vast majority of students qualify.

If you are a felon, once you are released from jail, you can still qualify.

The only people who really can't qualify that I'm aware of are non residents, people who have been convicted of drug offenses that occurred while accepting federal financial aid, and people who already have degrees.