USB stick appearing as hard disk drive, not removable storage device

The problem, appears, is not Windows but the device itself. For some reason, the device is registering itself as a Mass Storage device, not a Removable Storage device.

A nifty program I found via this blog entry called BootIt solved the problem for me in a jiffy: simply switch on the "removable bit"! Unplug and replug, and you're set to go.

I understand there's a bloatware version of this program all over the internet. See if you can get version 1.07; that gets the job done.

Additional bonus of being able to switch the "removable" bit: you can partition your flash drive!

The drive's controller is what reports the drive as fixed or removable. So, this can only be set via utilities that can edit controller's data.

Reportedly, some manufacturers started to mark USB pendrives as fixed to make it easier to pass Win8 certification requirements (Sandisk specifically is reported to have reversed that decision since).

The BootIt utility mentioned in the other answer does exactly that. But it can only work with a limited number of controller models (one person mentions some Silicon Motion and Phison ones).

Your best shot is to find out your flash drive's controller model and use an industrial utility by its manufacturer. E.g. Silicon Motion's utility is called "SMI MPTool".

There are sites dedicated to collecting these. http://usbdev.ru has the best collection that I know of (by both content and organization) and also includes utilities to find controller model and tutorials.

E.g. SMI MPTool sets the drive as fixed/removable like this (USB-ZIP is removable, USB-HDD is fixed):

I must mention there exists another way - filter drivers that forge the removable bit in a drive's info - like diskmod. But that is only a temporary solution it this case. These drivers are best fit for other tasks - e.g. for a Windows installation running off a USB drive (so that it agrees to place a swap file there).