There are a bunch of What Day Is Your Pickup Day apps, on a city by city basis, and a couple that do the same thing for larger areas. That's not really what I'm looking for, especially since the times I have that question are usually weather related. It would be interesting to know whether those are just databases, or if they actually get push updates for weather related pickup day changes. Waste Management has an app that includes What Day info, account management features and a method for requesting a "bulk pickup" or an extra pickup. The bulk pickup categories for my account include: Furniture, Appliance, Large Yard Waste and the ever handy "Miscellaneous". Subcategories enumerate items of furniture (include Sofa with or without a bed), appliances, etc. Poking around in the app, I took a look at the holiday schedule and, in the course of hitting the arrow back, stalled and got an error message "Connection problem. Please try again" which suggests that while the app has some useful features in the front end and in terms of what kinds of services you can set up using it, it has some bugs that need to be worked on (hitting the "Home" button in the app -- not the apple button -- which in theory went to the same place, did work). The app does not appear to support "vacation hold" or "resume pickup" features, altho I think you _can_ do this by calling customer service.
Mr. Bin, in Canada, may also help schedule one-off pickups; I'm not sure.
A company called Spoiler Alert specializes in food: connecting food that is going to hit its expiration date soon, and people who might be able to use it. That's a great idea -- get a little money to one group, save another group a bunch of money, and reduce waste in the food system as a whole. It's exactly the kind of thing that makes the world a better place, while simultaneously reducing GDP. Our economic measurements really ought to do a better job of this stuff -- Spoiler Alert is a lot like a negative line count day for a programmer. Generally, those are our most productive days, but almost no one who measures productivity recognizes them as such.
A company called Rubicon does some of what I am looking for (enter an address, find a company that will pick up whatever you are trying to get rid of). They've been around a while, with a business focus. They did exactly what I wanted to see, which align incentives to divert: private haulers have to pay tipping fees, so they are motivated to find ways to get paid for something rather than pay to dump it (recycling). More recently, they got a city of Atlanta contract for 6 months to help the city with diversion.
Santa Fe is using them for data collection:
And then there are much, much, much smaller operations, such as Pick Pink in Manhattan, Kansas:
With Waste Management -- the biggest residential trash hauler in the US -- offering a somewhat credible app and service associated with it, it will be interesting to see how companies like Rubicon and Spoiler Alert evolve. According to a source from 2006 linked from the WM wikipedia entry, WM + Republic handle about half the solid waste in the US by volume. However, as near as I can tell, Republic is smaller than WM, and I don't think they serve half the households in the US, so I've got my doubts about some of these estimates (estimates associated with solid waste in the US specifically, but everywhere, really, tend to be really not very accurate, shall we say? Or even comparable).
Until a few months ago, my WM service involved guys lifting the bins; that has since been automated (so it's a guy driving the truck and there is a claw that lifts the bins). Solid waste associated truck fleets are among the largest truck fleets in the company. This is clearly an area ripe for further automation.
ETA: I wanted to mention "Donation Town", a website not an app, which I ran across. It is a really interesting idea, but too lightly implemented to be useful (as yet). Type in a zip code, find out who does what kind of charity pickup in your area. This kind of data is still way too distributed; it would be a huge project to get it all into some kind of database and make it usable by a service and related app.