Conical Springs
A compression spring may be conical. In this case, its main feature is that it may be only the thickness of a single coil at solid height.
Conical springs from RAPIC are made from wire diameter 0.2mm to 20 mm with or without ground ends, depending on wire diameter and the quality of guide required.
Hourglass Springs
Also known as biconical springs, these are often used in sprung mattresses.
Barrel Springs
These are cylindrical springs with smaller coils at each end, producing a barrel shape.
They are used in vehicle suspensions and as shock absorbers in machinery. They are also used in mattresses.