Check backgrounds on new workers.
In addition to potential legal problems, for most jobs some recommendation contacts and employment history are desired. Leaving these unchecked implies that you did not really need the information on the form and don't care about what they really did before, even if they were fired for criminal violations or harassment of other employees. If only for workplace safety, not doing a basic background check is a very risky approach.
Check backgrounds for key workers.
Criminal background checks are required for workers applying for certain jobs involving various kinds of trust, like school teachers and bus drivers. For workers doing sensitive government work, background checks are a required part of the security clearance process. For workers who have a high degree of sensitive access, or in whom great trust is placed more intensive background checks may be called for.
Check other worker backgrounds.
Citizenship or work permit checks are also required for almost any legal job in the U.S. But many employers do the absolute minimum checking required; verification that a valid social security number was provided for tax purposes, and verification of a bank account for direct deposits of paychecks.