Summary

Bring a piece of ancient history into your kitchen by printing this authentic stone age towel holder ;-)

If you are looking for a simpler, smaller design, have a look at http://www.thingiverse.com/thing:706767 as well!
But if you like cartoons, silly contraptions and don't mind sacrificing a few pen springs (see instructions), you know which one I'm gonna recommend...

Instructions

The design prints in 4 parts (unfortunately, I couldn't think of a way to make it completely support-free for the larger parts) and won't need much assembly.

In order to change towel rolls, you need to be able to pull the axis pieces apart. I suggest you mirror the STL so that the rather bulky-looking moving part faces away from the room...unless you really like that look. Find two springs (e.g. from old pens) that are about 20x1.5 mm - the typical size of springs I found in my pens and therefor the one I used when modeling. Next, stick these springs into the long holes in the smallest part (red piece on the far right in the renderings) and make sure the won't come out of the side. If they do, you should still be able to get this part to function by using a large washer when you mount it on the wall, thereby covering most of the spring channels.
IMPORTANT - before you mount the moving part to the wall, make sure the distance to the other part and the length of the springs allow an easy exchange of rolls while maintaining stability in the relaxed state - you may need someone to help you with holding everything in place. If the springs are too strong, cut a piece off and stretch the remainder back to the required length.

Now mount everything on the wall, again checking the ease of movement from time to time and especially before tightening the last screws.

Stone Age Kitchen Towel Holder