EDIT Check out version 2, it's way better.

I made this for my wife's Samsung Galaxy Note 5, with the wireless fast charger (model EP-PN920). This puck is slightly larger, and a slightly different shape, than the older non-fast version. I couldn't find anything appropriate on Thingiverse, so I made my own in Tinkercad. She wanted something so that she could watch Netflix in bed, while charging, without having to hold it. It also doubles as a nice bedside clock if you turn on daydream in the android display settings. You can set the phone in either portrait or landscape.

The Note 5 is pretty tall, so if you wanted to use this with a smaller phone, I'd strongly suggest dropping the hole section down a few mm (or alternatively, raise the base points of contact). I've noticed with my Galaxy S6 that it's right on the edge of detection in both portrait and landscape.

Here's the Tinkercad link so you can modify it as you please:
https://www.tinkercad.com/things/1kN9UPh1wjZ

EDIT 20160401:
I'm working on version 2 right now. reduced the width, dropped the charger down a few mm to work with more phones. I haven't had a chance to print it, but you can tinker with it here:
www.tinkercad.com/things/9K8pJOggG5B
I'll remix the original when this one is satisfactory, and link it here.

EDIT 20160412:
v2 (w/cover) can now be found here, until I can print it:
https://www.tinkercad.com/things/1iTt6qQjqjq

EDIT 20160414:
v2 can now be found here:
http://www.thingiverse.com/thing:1489562