Why isn't it possible to locate the rudder in front of an airplane's center of gravity?
Effect on Aerodynamic Coefficients

It is possible to locate a vertical fin, as well as a control surface, ahead of the center of gravity.  $c_{n_r}$ (yaw-induced yawing moment or yaw damping) will not likely change much, all other things being equal. $c_{n_\beta}$ (sideslip-induced yawing moment or directional stability), on the other hand, will be reduced, perhaps becoming negative. Any sideslip will therefore result in a yaw moment which increases the sideslip.  Expressed in linear control theory terms, this will be a pole in right hand plane when you plot the complex solution of the equations of motion. It is an unstable configuration.

Active Control

As Peter mentioned, it is possible to remain in control in this configuration by means of active control.  Active control tends to be somewhat tiring for a human operator if it is possible at all.  Incidentally, this kind of instability existed in the lateral axis of the 1903 Wright Flyer, which was configured with a canard of considerable proportion. It was reportedly quite tiring to keep stable.

CP ahead of CG

There are advantages to having a center of pressure ahead of the center of gravity, the chief being agility.  Back in control terms, the farther you move poles to the right, toward instability, the faster or "twitchy-er" the response.  The F-16 is configured this way and has been the standard of maneuverability for quite some time, requiring computers and fly-by wire for stability augmentation.  

Control surfaces ahead of CG

It is also advantageous for maneuverability to have control surfaces ahead of the CG.  In this case it is for avoiding a feature of control termed "non-minimum phase" response.  For a conventional, tail-configured aircraft, when a climb is commanded, the tail is forced down, leading to a net reduction in lift until an increase of angle of attack is developed.  This is non-minimum phase response.  It was necessary to initially go the opposite direction from that which was desired.  In canard configurations, this is not the case, first the nose climbs, then everything climbs.

Put them together...

Forward control surfaces, forward center of pressure and a stability augmentation system with adequate dynamic pressure make for one heck of a maneuverable package.  This is a common recipie for tactical missiles.