Can I use a supercapacitor (like Maxwell boostCAP 3000F) on a coilgun?
Let's try it! 

From the datasheet: 


Capacity : 3000F
Absolute Maximum Current : 1900A


Now the charge stored, Q, = C * V = 3000 * 2.7 = 8100 Coulombs.

So at Abs Max Current (1900A) discharge time can be as low as ...8100 / 1900 = 4.26 seconds.

So divide the length of the gun by 4.26 seconds to get the muzzle velocity.

For any reasonable size of gun, you could walk faster than the bullet.

(Edit : I am being a bit unfair : if 1900A is a useful current in launching a small, er, mass at high velocity, then the capacitor can launch a number of small masses over a 4 second burst. But as far as dumping all its energy (10.9kj) into one mass is concerned, that would take 4 seconds, for an average power about 2.5 kw. That's really not much by projectile launching standards.)