Would it be feasible to let the core/photon act as a USB-Drive/USB-Memory-Stick when you connect it to a computer?
This would open a whole new range of things to play with. Combined with an SD-Drive, one could do some crazy stuff… 
I am not sure if this other post is related? USB HID support on Core?
Feasible? Yes. Has anyone done it for the core? No 
I would look to see if anyone else has used the microcontroller in the SparkCore/Photon to implement a USB Mass Storage setup. Please report your findings!
As far as I know implementing a USB Host is very complicated. A mass storage implementation (FAT/32) nearly impossible.
Maybe this product is an option , works extremely good.
A quick google search suggests that not only is it possible, it’s been done.
Links:
https://www.google.com/search?q=stm32f103+usb+mass+storage&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a
http://www.keil.com/download/docs/362.asp
Wow. As a full usb host, this is amazing.
Please note: as far as I understood, the question was a USB Host, which means: you can use an USB stick to write data from the Spark to the USB Stick. The Project mentioned are about a Spark acting like a USB Stick when inserted into a PC.
This was my misinterpretation!
We are using such components to use the Spark as a data logging device (with exchangeable mass storage)
For arduino there is a special shield available to use USB sticks
http://arduino.cc/en/Main/ArduinoUSBHostShield
I believe @Coffee was asking if Spark could act as a USB Mass Storage Device not talk to USB Mass Storage Devices. Have I got something confused?
No, you are correct. Was my mistake.
Actually, what about making the photon into a mass storage device (acting like a USB stick) using a linked SD card or something?
Do you guys have any pointers?
Has anyone been successful with this? I would like my Particle Photon to act like a USB drive. When I plug it into a USB slot it will actually connect to a PC over my WiFi and access files from a folder.