Depends what country you're from ... a lot of countries have a Rehabilitation of Offenders act or something similar that automatically wipes your criminal record clean after so many years. In the UK / Australia / New Zealand it's normally 7 years. There are obviously some crimes that do not qualify to be removed from the record.
But I would imagine, if you furnish a clean criminal record certificate from the police, there really is no way they can check up because it's removed from the system forever.
You would need to be careful though, for example if it was something to do with drugs, and you tried to travel to the USA during that time and they refused you entry because of your criminal record, that will be in the Yank system forever, regardless of what your home country did with your record. A cousin of mine had that problem, he did something silly when he was a teenager, he's now a respectable and successful hospital surgeon, but he can never travel to the USA, even though it's been decades since his record was "wiped clean" in his home country.