This page will attempt to discuss the many different types of valves used in pneumatic launchers, each briefly. They are ordered from a perceived "weakest" to "best".
The simplest valve of all, but not always the cheapest, depending on the size needed. These are the slowest as the user typically has to turn the handle 1/4 turn to fully open the valve, which can be difficult for larger valves with more friction especially. Often, the projectile has left the barrel before the valve has been completely opened.
A suggested and often implemented improvement to the ball valve is to use a mechanical means of opening it, such as a heavy spring and pin to pull the valve open, or a pneumatic ram (but if you are able to utilize or build a pneumatic cylinder then you should have no problem using a better valve!).
I would not suggest a ball valve for anything but the dinkiest small launchers, or launchers too big for a better valve to be practical. Even then, I would suggest spring loading the valve.
These are typically used for water (although air solenoid valves are available from industrial or mechanical supplies) and use a basic diaphragm valve to operate.
A sprinkler valve is the most common used, and is easily modified to be purely pneumatically actuated.
In its stock state, a sprinkler valve uses a 24V solenoid to unseat a small piston from a vent hole above the diaphragm, which allows the pressure to drop low enough for the diaphragm to unseat and allow flow from the inlet to the outlet.
However, by either removing the solenoid and plugging its hole with epoxy (or simply leaving it there and not using it), and then drilling and tapping a 1/4" NPT hole to the lid, the valve can be pneumatically actuated in the same way as the solenoid, but much faster and without the use of batteries.
These are used on pneumatic cylinders to quickly relieve pressure on the side of the cylinder opposing the desired movement, during a switch in direction or retraction of a single acting cylinder.
There are three sides, the IN (pilot) side, the CYL (cylinder) side, and the EXH (exhaust) side. During filling, air flows from the IN side to the CYL side fairly quickly, due to the shape of the piston/diaphragm in the valve. This allows the cylinder to actuate as normally. However, when the piston needs to retract (for a one-way cylinder) or change directions, pressure is relieved from the IN side of the valve, which is now completely sealed from the CYL side. This caused the diaphragm to unseat and exhaust the cylinder to the atmosphere.
It isn't too much of a stretch to use these in cannons. The CYL side is connected to the air chamber, the EXH side is connected to the barrel, and the IN side is connected to both your fill and pilot valves. You will discover that these valves are remarkably similar to outlet sealing piston valves.
These are grouped together due to their similarities and not on operating principle.
This is just a quick overview, as I plan for a more in-depth explanation of this section as well.
A piston valve can be either inlet (chamber) sealing or outlet (barrel) sealing. Both have their advantages, but the outlet sealing type is much easier to make for the beginning hobbyist, and often quicker and more efficient.
Piston valves operate in much the same way as a Q.E.V. valve, which is by a created pressure differential, which forces the piston back, unseating the outlet or inlet, and allowing air to flow through the valve into the barrel.
Outlet sealing valves have more in common with Q.E.V.s, but can rarely approach their efficiency without serious dedication to build quality. However, Q.E.V.s can in fact be modified to be inlet (chamber) sealing valves, demonstrating the close similarity to piston valves of both types.
These are so named because of their shape. They are (usually) manually actuated, and contain a balanced piston (shaped basically like a "spool", hence the name). They often reside in the barrel or a section of tubing the same diameter as the barrel, and cover a series of ports with the same total cross-sectional area as the barrel. When the spool is pulled back (often by a rod), the first port is uncovered, allowing air pressure on the front of the spool, forcing it back to uncover the rest of the ports and allow air through the barrel.
These are typically marginally more efficient than standard piston valves because of the lack of a pilot volume, so there is no residual air behind the piston to prevent it from opening as quickly and completely as possible. However, there's not much evidence as to the extent of any performance increase, and a properly built piston valve can negate this fact further.
Both of these types of valves involve safety considerations and quality build materials during construction, due to the large energies pistons and spools gain during acceleration. More on this later.
These are theoretically the fastest valves you can use, although burst disks can have a problem with the disk remaining partially intact and blocking the barrel port slightly.
Burst disks can be triggered in a number of ways. The simplest way is to simply fill the chamber until the pressure bursts the burst disk. This can be rather nerve-racking (especially with inconsistent disk materials) but it works, and is often the simplest and cheapest solution for larger cannons.
Burst disks can also be pneumatically and mechanically triggered. To be pneumatically triggered, two burst disks are used to block off a small volume of air between the main chamber and the barrel. The volume is filled to a moderate pressure, and then the chamber is filled past the disk's bursting pressure. Because of the moderate pressure on the other side of the disk, the disk on the chamber side has a net force not strong enough to break the disk. This small volume of air between the two disks is vented to the atmosphere, at which point the chamber pressure overcomes both disks and is exhausted through the barrel.
Mechanically triggered burst disks require either pre-made pneumatic cylinders or tedious construction and a number of seals. They use a mechanical implement such as a blade or "cookie cutter" which punctures the disk.
Detent type launchers use the projectile as the valve. The projectile either seals perfectly in the barrel, or is pushed against a detent which forms a seal with the projectile. The detent is either mechanically moved or overcome by pressure, and the projectile exits the barrel with virtually no valve opening times and little flow restriction.
While there are a number of valves to choose from when designing your launcher, the most important factor should be practicality. If you are building a 1/2" barreled launcher, a Q.E.V. would be a wise choice, but for a 6" barrel, a burst disk or butterfly valve would be more practical.