Can I travel to the USA on holiday with criminal record.?

probably not but depends on the record perhaps

In general, YES you can. The exception would be if the/a judge ordered you NOT to travel out of your area or state. If you are on parole then usually you will have to inform and ask your permission from your PO. He or she will get/give an order to allow it.
But if you have a straight up cleared or completed your sentence with no parole you have the same rights to travel as anyone.

More information needed.
Short answer ... if minor crime committed a year or more ago, probably no problem. If major crime, recently committed crime, or drug related crime, probably not.

Long answer .... in some cases with special permission you can, you will have to check with a U.S. Embassy on the procedures for applying for this.

I believe the previous answer was referring to a person from the U.S. traveling within the U.S. so disregard for your purposes, of coming to the U.S. from another country.