<p>Let's say you're printing a container or some other object with no infill. What's a good rule of thumb for how thick to make the outside? I'm looking for something along the lines of millimeters thick per square inch of area.</p>

<p>I'm thinking about PLA right now, but answers for ABS and other materials are welcome, too.</p>

I make small objects (25mm^2) with 1 to 1.5 mm walls and larger objects (think coffee cups)  with about 2.5 - 3 mm walls.  I set the line width and number of perimeters to completely fill the thickness. 
I use this for ABS and PLA.
The PLA objects have been electronics enclosures,  with internal structures to support the parts.   They aren't subjected to strong forces.   I've made small containers for stain gauges with the amplifiers,  and larger ones for greater sequences and Arduino boxes. 
I've used ABS also for coffee mugs and beverage glasses,  to withstand the mass and temperature of drinks. 
It can take some fussing to worry the Slic3r slicing parameters into place.  Especially with mugs the design is for function and appearance,  not for effect.