I have been using LABite.com for my food delivery needs over here in Echo Park for the last few months. They say they have been servicing LA since 2001, but I think they must have recently expanded their service area. I seem to recall them saying nay to deliveries this far east about two years ago.
At any rate, recently they have delivered lovely meals from Vermont, Daily Grill, The Grill on Hollywood (which has jumbo lump crab cocktails, hence the distinction) and Kazoko Sushi twice, both times were very serviceable.
LABite has a laundry list of restaurants in several price ranges, they calculate a service fee and a tip (ok, ok, it's not their restaurant that is profiting from the food purchases so I get the necessity), and the driver never tries to get you to tip him extra at the door, nor will he even let you if you try.
Check it out, readers. LABite.com.