Drugs you can show completion of a program, swear you've been clean for two years, have testimonials from your preacher, rabbi and yoga instructor.
Theft is tougher and would probably be a bar for any financial company (except apparently at the top executive levels). Might be better to lie or not check either "Do you have a criminal record" checkbox and hope they don't do the background check.
Violent crime, property damage stuff you can just give your side and claim that it was a minor offense and the other party was out to get you. Doesn't look good if you have multiple offenses, though.