Not in a fast-food restaurant, no.
You'll often see folks in cafés help out and return their trays, but it's not a guarantee - and in some establishments it's not even possible for you as a customer to do this. At the end of the day, you're paying to sit down - and clearing your table afterwards is priced into the food offer.
Fast food is a bit more of a grey area, since there's not necessarily table service. I'd throw away my rubbish at e.g. Burger King - there's usually bins provided for this purpose.
I don't think it's really all that outrageous to just leave the detritus on the table in either case. But when there's no table service, the tables won't be getting cleared so regularly, so it can make things inconvenient for the other patrons.
I would clean up after myself somewhere like McDonalds or Burger King, though in a cafe or restaurant I wouldn't. In a restaurant I usually put the plates together to make it easier for the waiter or waitress to clear the table and try not to be too messy.