Denied exit from the US is possible under these circumstances. These are not the only reasons, but are usually the primary ones.

1. Federal income tax issues whose dollar amount qualifies as a felony. And I don't just mean you owe XXXX and haven't paid. You have done something that can be prosecuted criminally.

2. Those on probabtion or parole without written permission from the parole or probation officer

3. With a child in tow that is the subject of a custody dispute or non custodial parent does not have written permission from the custodial parent -International Parental Child Kidnapping Act

4. Unpaid child support in an amount that qualifies as a felony