The white reflector provides the softest, most natural-appearing light. The reflected light is very diffuse, and matches the colour temperature of the ambient (or main) light. Except when it is used as a main front light on a backlit subject (and similar situations) it doesn't add any noticeable highlights or shadows of its own, apart from a soft catchlight in the eyes (or other elements of the subject that have specular reflection). Used as a main light source, especially as a front light, it may be too "flat". Its main failing, though, is that in order to provide enough reflected light for many shots, it needs to be very close to the subject in relation to its size. It may not be possible to both frame and light the shot the way you want using a white reflector.
The silver reflector has a lot in common with the white reflector, except that it is more reflective and usually much more directional. The light from a silver reflector is "hotter" (it is more likely to cause noticeable highlights and shadows), but it also has a greater reach (the reflector can be farther away from the subject). You can get much lower lighting ratios (the range of light intensity falling on the subject) using single-light setups using a silver reflector than using a white reflector. Because of the directionality of the reflected light, it can reveal texture better than a white reflector -- but that's a two-edged sword, since it also reveals skin problems. Placement and aiming are also more critical than with a white reflector; outdoors it's almost always necessary to have an assistant hold a silver reflector rather than just clamp it to a C-stand.
The gold reflector had all of the lighting characteristics of the silver reflector, except that it radically shifts the colour temperature. In the film days, it would be used to give people a healthy tanned appearance, lke using an 81C warming filter, but without affecting the rest of the scene. It can still serve much the same function, but it will often look unnatural unless the overall light is balanced very cool (like "north light" -- indirect sunlight from a blue sky, which is often at 6500 kelvins or more). Note that the gold reflector will shift the colour temperature of everything it hits, so if you're photographing a model wearing white, and that white has to look white in the final picture, you're just going to have to put things back the way they were in post anyway
The zebra reflector (the one striped silver and gold) is a better compromise for warming the colour temperature of the reflected light in many circumstances. It adds that glow of tan, but not to the same degree as the gold reflector.
The scrim is not a reflector (although a white one can be used as a reflector in close if you're really in a pinch). They come in a variety of materials, each used for a slightly different purpose. A white, tight-weaved scrim (one you can't see through clearly when you hold it close to your eyes) is used most often to soften a harsh light source. Think of it as a shoot-through umbrella (or a softbox) for the sun. This is the type normally included in a multi-reflector kit. It will allow you to take pleasing pictures of people in lighting that would normally be far too harsh. (White scrims used in the movie industry can be the size of a large event canopy/tent, but are usually of a looser weave so the sunlight isn't comletely flattened.) It does, though, hold back a considerable amount of light, so you need to be careful balancing your subject and background (no scrim is that big).
That's where the looser-weaved varieties of scrims come in. Often, they are black rather than white, and they are place behind the subject you are lighting. Think of them as a neutral density filter that affects only the background. (A white one will also brighten and reduce the contrast of the background.) It's not likely you'll find a black scrim in a 5-in-1 kit, but it's worth including for completeness.
The black "reflector" is quite emphatically not the same thing as no reflector at all. Its task is to prevent uncontrolled reflections from falling on your subject (or other elements in the picture). It is often used to increase contrast, but it can also keep that lovely mint-cream green wallpaper from giving your otherwise carefully-lit subject a sort of undead pallor.
As always, I invite edits and suggestions for editing -- the point of the game is to have the best answer on this site, not reputation or self-promotion.