I deliver pizza right now as a part time job. At my place we charge a $1 delivery fee. If the driver is new (less than 2 weeks) they do not get the $1. If they have worked there for 2wks-4wks they get 50 cents of the $1. After 4wks they get the entire $1. On top of that we get paid $5/hr and keep all of our tips. However we do use our own vehicles and pay for our own gas. By my calculations the $1 we get per delivery pretty much covers gas + wear and tear. So yes you should still tip because if you didn't we would only make $5/hr after expenses. Which is less then minimum wage and would suck.
Fortunately my average tip is $3