Gate valves are an oldie, but still a goodie. Chiefly used for commercial, industrial, and institutional applications these days, gate valves feature... well, a "gate" (also referred to as a wedge, or disc) that when lowered, seals off the flow. When raised, it's retracted into the body of the valve, which means no loss of flow; the inside diameter of the valve matches that of the pipe it's connected to. This is all controlled by a wheel handle, and can be of the "Open Stem and Yoke", or the "Non-Rising" varieties: with an open stem and yoke, the handle moves down the stem with the gate; non-rising stems remain fixed. The clear benefit of the open stem and yoke is that you're given an indicator of the valve's status: if the handle is down, you know it's closed. However, depending on the size of the valve, there may not be enough space for its operation: enter the non-rising gate valve.
This type operates using a stopper, which is lowered onto a baffle, blocking flow. Because of the space the baffle takes up inside the valve, flow is restricted, making these exactly the wrong type of valve to use in a full-flow situation. They are, however, good for throttling and are not bothered by frequent operation.
Probably the most widely-used valve design, ball valves employ a cored, rotating ball to control flow. Usually operated by lever handle, they also offer a quick view of their status. Their design makes them ideal for full-flow applications, and their easy, low-wear operation is also excellent for throttling. A quality ball valve can be opened and closed a hundred times a day with little impact on the valve mechanism itself, so you can expect to get a long life out of these valves with very little maintenance or trouble. They come in a very wide range of materials and styles, including brass, stainless steel, PVC, threaded, and push-to-fit, to suit almost any application.
The butterfly moniker refers instead to the mechanism inside, essentially a disc that rotates by handle turns; this of course means that flow is reduced through the valve. Although these valves can be used for throttling – some include locking mechanisms on the handle to counteract the force of water on the disc – they are best utilized fully opened or closed. Among the valve types, butterfly valves are compact, with relatively short bodies, making them significantly lighter than other types. Keep in mind, however, that these valves rely on a gasket which will eventually need replacement.