1: What's on the rags?
  a: oil/finish:  Store in metal container away from anything flammable.
  b. H2O: let dry in air
Oily rags can self ignite. also activated epoxy in cups can too. Many of us have been fortunate to not burned down house/shop due to droppong rags on floor or in wood chips.

Glenn J.

The problem of disposing of oily rags self-combusting and starting fires comes about when there is a large mass of oily material.  The process of drying (to be correct, polymerization) is exothermic - it gives off heat.  If that heat is concentrated, it can cause the mass to combust.  So the basic principle is to avoid high concentrations of oily combustible material, and also to avoid close contact with other flammable material while it is polymerizing.

I don't use fabric rags - instead, I use paper towel and toilet paper to apply finishes and for cleanup in my shop.

But my approach is very similar to Bill - I have a garbage can in the shop with a plastic bag liner, and I prefer wipe-on  oil finishes.  When I complete the finishing process, I lay the bit of oily paper over the edge of the garbage can.  When it becomes dry and stiff (typically a day or so), I drop it into the can/bag to eventually be thrown out with whatever else is in there. 

Because I mainly do turning, the bits of oily paper I have to dispose of are fairly small (perhaps 4" square), and they dry quickly when spread out in open air.  I don't worry about doing that in the shop because they are so small, and each bit is spread out and isolated from any other flammable material until it has dried. 

I do understand however that the folks who do larger projects and have more (and larger) rags to dispose of may need to take more precautions such as drying their stuff out doors.  Really careful folks put their oily rags in containers of water to dry (actually, polymerize - that will happen even if the rag is in water) but I don't think that is necessary in my situation.