It should be noted that there are several different types of barbell, which are suitable for different types of body piercing.
Straight barbells are, as the name implies, straight bars of metal with screw-on balls on either end. These are usually worn in tongue piercings1. Contrary to popular belief, they are not generally suitable for eyebrow piercings or surface piercings; the flat skin combined with the straight bar puts too much pressure on the piercing, eventually causing rejection.
Curved barbells, also known as navel or banana bars, are usually worn in navel piercings. These are, fairly obviously, slightly curved bars with screw-on balls.
Circular barbells are horseshoe-shaped, and are commonly worn in septum piercings.
Surface bars are square-bracket-shaped barbells specifically designed to prevent rejection in surface piercings, by reducing the pressure of the jewellery against the skin.
Labret studs could be considered a type of barbell; these are bars with a flat disc on one end and a screw-on ball or spike on the other. They are worn in lip piercings.
Barbells can be made out of various metals including surgical stainless steel, titanium, gold, and niobium. Sometimes, they are made of non-metals; for instance, surface piercings are sometimes done with a tygon bar for flexibility. Nylon and acrylic are also a possibility. They are not suitable for all piercings; some would be better with a captive bead ring.
1 I haven't listed every possible piercing for each type of barbell for the simple reason that I don't know.
Sources? I read BMEzine and the Livejournal piercing community a lot.