1-800-GOT-JUNK?

We couldn't get a bin because we have a fire hydrant on our lawn. So, we piled the junk in back as we did a major reno project. We had Got-Junk remove the stuff in 4 different trips (old lath/plaster, wooden frames, concrete, etc). The staff were always friendly and helpful, they give you a max price before starting the job, and they sweep up afterwards.
The cost was higher than getting a bin, but reasonable compared to other junk removal companies.
And, they give you a 2-hour window for when they will arrive (eg. 1:00-3:00) and then they call you 15 minutes before that to give you a more accurate arrival time! A very nice touch!!