Among others. It is a stpale lens for most photoographers. It is very good in low light conditions due to its large aperture. You can use them for alot of things, those three are probably the most common but they are not then end.
50mm is the standard "normal view on 35mm film. Shorter than that is considered wide angle and longer is considered telephoto.
For some reason, 50mm lenses are the cheapest to buy. Maybe it's because they are cheap to make...or maybe it's because there are so many of them....but it's the cheapest way to get a nice wide aperture of F1.8
50mm 1.8's are great lenses. The biggest plus with these is their price. There are very, very many of them out there so prices stay low. They "see" like your eyes see, so the shots look can look very natural. With my 50mm I also sometimes use a 2x teleconverter to get me a nice low telephoto.
Before computers it was really hard to make a good zoom lens that anyone could afford, and the standard lens a 35mm SLR would come with was a 50mm f/1.8 (or something close). For me the main reason to carry a 50mm f/1.8 is that it's a cheap (often the cheapest lens in any line) and speedy companion for my zoom lens for using in low light conditions. With my x1.6 DSLR it's a good portrait lens.