Chain drop under load
Edit: @Qwirk: If you look at your photo, where the chain is resting on the small chain ring, do you see the gaps between chain and teeth? that is a key indicator of either extensive chain wear, extensive chain ring wear, or both. In this case, based on the appearance of the upper chain ring, I'm going to say both.

Those are the first 3 options I'd look at, as well.

Have you replaced your chain recently? If so, the new chain may not be meshing well with the old chain rings.

To figure out which, first check the chain for wear. 

If it doesn't show any serious chain wear, compare the chain rings on your bike to a set of new chain rings. It doesn't have to be shark toothed to e worn, but that is most common. Hooking, or simply teeth that are significantly shortened will cause similar issues.

Check as well for bent or missing teeth in the chain rings. This shouldn't be the case because it's happening in more than one gear, but it could still be. Also, check the rear cassette for missing or bent teeth, for the same reason.

Last, if the rings do not appear worn, you should replace the chain, (or soak it and re-lube it at a minimum). This will eliminate the possibility of a burr or a sticking point in the chain that is more subtle than a stiff link.

Oh, and a bent hanger would have to be pretty visible to cause this kind of activity, but it's still worth checking.

Hope that helps.