How thick is 0.1 mm? I have a printer with a 0.1 mm typical layer thickness. Of course I can choose some different sizes in Cura or other slicing software, but most prints on this machine will be .1mm. In my (admittedly limited) experience thus far, the 0.1 mm seems typical for other printers, too.

I want to get a sense of just how thick this is. I know about the paper trick for leveling the print bed, but my understanding is the first layer pushes into the bed a little, meaning it's less than 0.1 mm and so paper isn't a good example for the typical layer. 

Is there a similar item with close to 0.1 mm thickness I can use to visualize this?
I'm not sure exactly what you mean by your comment to Davo's answer, but with respect to your use of a sheet of paper reference, it seems like you can still use 80 gsm paper as a reference for 0.1&nbsp;mm layers.

From Paper Sizes Explained (emphasis is mine):


  There is no universal calculation for the thickness of paper based on the gsm as varitaions in paper composition can affect the weight, so two different brands of 120gsm paper could have slightly different thicknesses. However, an average sheet of 80gsm paper, the most commonly used weight, measures approximately 0.1mm in thickness, which means that 10 sheets would measure 1mm. By comparison, 10 sheets of 120gsm paper would be 1.5mm thick, assuming the paper composition was the same.


So, given that:


80&nbsp;gsm => 0.1&nbsp;mm
120&nbsp;gsm => 0.15&nbsp;mm


Then 


40&nbsp;gsm => 0.05&nbsp;mm
60&nbsp;gsm => 0.075&nbsp;mm


From A Guide to Paper Types and Sizes

Paper Weight Descriptions

Weight        Feels Similar to:

35-55 gsm     Most newspapers
90 gsm        Mid-market magazine inner pages
130-250 gsm   A good quality promotional poster
180-250 gsm   Mid-market magazine cover
350 gsm       Most reasonable quality business cards


So, it would appear that you could use a newspaper sheet (or two) to test for layers of less than 0.1&nbsp;mm.  Obviously this would depend upon where in the world you are, and the (physical) quality of your newspapers. Here in the UK, or rather Europe, the exported version of the Guardian used to be printed on some extremely lightweight paper (almost transparent tissue thin), in order to keep the costs of transport down to a minimum. So a folded sheet of that would certainly be in the range of 0.75 - 0.99&nbsp;mm (which seems to be the range that you are looking for). However, given that the printed media (as opposed to the online version) is currently in decline, I am not entirely sure if it is still available.

Or, how about grease proof paper? From the Wikipedia entry:


  Basis weights are usually 30–50 g/m²


Although, this paper has been processed (supercalandered) and treated with starch, which will increase the density, so the thickness will not correlate to the table above (i.e. it will be thinner).

Giftwrap paper (not the really thick stuff) could be another option.

After having doing some long winded googling, I guess that the best bet would be to get hold of a micrometer and measure whatever paper yourself, as the specifications of paper are generally given in gsm and not mm (which is a bit annoying), and so it is somewhat difficult to provide you with a definitive answer (without physically measuring it).