This parametric paper cup dispenser will generate cup dispensers for any size paper cup. Just open the .scad and change the values in ALL_CAPS. It even includes a mounting bracket (which is also parametric!).

By default it's configured to generate a dispenser for 5oz Dixie Cups and pre-generated .stl files for that size cup are included.

It works just like any paper cup dispenser: There's a lip at the bottom that prevents the cups from falling out but if you give the cup a little tug it should come out while leaving behind the remaining stack of its brethren.

EDIT 20181119: Gave the .scad an overhaul to better support more parameters! It's also much better about setting arbitrary thicknesses and heights. You should be able to control just about every aspect now! There's also detailed variable names (with comments) instead of hard-coded values for basically everything. Please post a comment if there are any issues!

Print instructions

Infill doesn't matter much... Only for the cap. I used a 0.6mm nozzle for my print in the picture but it's nothing fancy--it'll print fine with whatever you've got.

Layer height is to your preference. The 45° angle bits will probably look best with 0.2mm or below though. Really doesn't matter much though! If you're lazy and you have a big enough nozzle I bet you could even get away with 0.5mm layers!