Don't Work Overtime for Free
It can be tempting to work overtime so that you're perceived as a team player but to feel guilty asking for payment for these hours. It has been my experience that this sets a bad precedent and you should almost always bill for any time that you spent working.
To avoid complications, ask your manager for an explanation of the process you should follow when overtime becomes necessary. Don't wait until after you've worked the overtime as this puts undue pressure on the manager. Usually, the manager will just want to know ahead of time if you're going to exceed the regular agreed upon weekly amount e.g. 40 hours.
If you haven't received permission to work overtime, but your employee peers are staying late to wrap something up, wish them luck, but don't rub it in their faces that you're leaving and they aren't. If you have some warning of an upcoming push where you think your co-workers will end up needing to put some extra time in, try to slip in a comment nonchalantly that you're actually not allowed to work beyond a certain number of hours. That let's them know that it's not your call even though you'd certainly be willing to stay.
If you're in the beginning stages of working on a consulting project, make sure you read another post about not working for free.