Is there a way to assign a function (like cut/copy/paste) to the middle mouse button or scroll wheel in Windows 7?
X-Mouse Button Control is a windows application to remap your mouse buttons. This software can handle, including things like copy, cut, and paste, volume control, media player control, send a custom keystroke sequence, launch your email (or any other) application, capture screen (or active window) image to clipboard, click-drag, and save and restore desktop icon positions.
Out of the box, no, the mouse button is used for putting the machine in scroll mode. If you have a Microsoft or Logitech mouse, there is some driver software (eg Intellipoint) that allows greater customization of the mouse buttons (including middle scroll button).
You can however find software (usually free) that gives you some of this functionality. The most popular of these is: X Mouse Button Control: http://www.highrez.co.uk/downloads/XMouseButtonControl.htm
Another possibility is to use AutoHotkey and assign the middle button to the action you want to perform. The example below sends a "back" signal when on a web page (to visit the previous page)
; Wheel click = back on navigator