depends on the situation
depends on the severity of the situation, timing in relation to your filing date. i.e. a simple DUI 20 years ago with a $30 fine and 24 hours in jail, will have less impact than a conviction for DUI in the week prior to the filing of your N-400 where the judge gave you $500 fine 6 months jail, suspended and 5 years probation.
Presume INS knows about the conviction, provide certified copy of the arresting disposition, the court disposition with your application.
Note: present rules prevent the naturalization of an applicant who is on probation, so filing N-400 before the end of your probation could be a waste of money....