They range from the very casual and sports-wear styles to relatively formal. The more casual pull-overs are usually "hoodies", or long-sleeved, jacket-type garments with attached hoods that are pulled over the head. As its name would indicate, a pull-over does not have zippers, snaps, or buttons.
Because of their knitted, rather than woven nature, they are more stretchy than other fabrics. Sweaters can also be of the pull-over type, as opposed to cardigans, which are usually fastened with buttons. Pull-over sweaters can be of a coarse, textured nature, such as fisherman's cable knit.
They can also be finely knitted with colorful patterns or designs. Pull-overs can be purchased in many styles and patterns. They can also be hand-knit in most yarns, from fine, fingering-weight yarn to chunky or bulky yarns. Pull-overs are so versatile that they can be worn at virtually any event or for any occasion, depending on the style. For casual wear, such as exercising or working around the house, a hoodie style or jersey knit would work just fine. For going out with friends, perhaps a slightly more sophisticated look would be preferable, such as a light, long-sleeved top for warm evenings, or a pretty, knit pattern in more of a sweater design would be appropriate. For formal occasions, most pull-overs would not be appropriate, because most formal fabrics are woven, not knit, and therefore would not stretch enough to be pulled over the head (according to Wikipedia).
However, there are a few knitted fabrics that could stretch enough to drape elegantly, as well as look sophisticated enough to be appropriate. For men, the choices are only slightly less versatile. Men can wear sweatshirts and hoodies just like women. For more formal wear, men can wear any variety of sweaters, from bulky wool to finely woven silk. Wool can be itchy, and some people are allergic. Cotton is much more breathable, but does not stretch as much. Silk and spandex are fabrics that drape very nicely and are thus more useful for formal occasions. Polyester and polyester mixes are very versatile and can be used for a range of garments. In short, pull-overs are extremely versatile clothing. They can be worn on many occasions, can be made from almost any fabric or yarn, and can fit most any budget, depending on the desire and need of the purchaser.