Types of fees:
Application fees: Above info is spot on, the only advice I would give is that higher fees means less applicants (we decided not to charge at all when we self managed, it did not add up to very much each year) and if it is non-refundable there are likely tenant-landlord laws about what you have to disclose about your criteria before they apply.
Late rent: If rent is late, there is an exra fee. Tenant-landlord law often limits what this can be.
Insufficient funds: If you accept personal checks and the check bounces, there is normally a fee.
Key/remote replacement fee: If new keys, garage door openers, mail keys, etc need to be replaced for the same tenant, there is often a fee.
Breaking lease: If a tenant moves out before the lease is over there is often a penalty clause. In most cases you cannot charge two different tenants for the same time period (double dip).
Pet fees/pet rent: Local laws vary, but there are often addiitonal deposits, fees, or rent for allowing pets that don't qualify as service animals or emotional support animals.