I don't like having the middle mouse button paste, because I often end up with uncompilable code in Eclipse. How can I turn this off (in all programs)? I'm running Fedora.
Having the middle button paste is a unix user interface standard, like having the left button select or activate, and the right button do something else (such as extending, toggling, firing up a menu, …). You'll find it bound to pasting in most unix applications.
If your problem is that your mouse is overly sensitive when you put your finger on the wheel, I suggest getting a better mouse. There are plenty of cheap decent mice.
You can reassign mouse button 2 to a different number. Applications identify the left, middle and right mouse buttons as buttons 1, 2 and 3 respectively. Put this code in a script that's executed when your X session starts (how to do that depends on your desktop environment).
It's a common convention that many programs abide by. There is no global way to turn it off, you must do it on a program by program basis.
EDIT: (short of, as Gilles says, disabling mouse button 2. But some programs do have other uses for mouse button 2, so I would not recommend this.)