(a) Knee braces immediately after injury
After surgery or injury, the type of brace prescribed is called an immobiliser.
It is just a fairly-heavy, padded, wrap-around support to stop the knee moving altogether, until the doctor has assessed the problem fully.
(b) Knee braces for 'unloading' one side of the joint
This kind of brace alters the forces going through a damaged side of the joint, possibly delaying the need for a knee replacement when arthritic changes are worse on one side of the joint than the other.
(c) Knee braces for ligament instability
This kind of brace is called a 'functional brace' and its purpose is to allow a certain amount of supported movement while preventing further damage.
This is the kind of brace you might see on a sportsperson, where the brace might be supporting damaged ligaments.
(d) Knee braces for patellar instability
Patients who have suffered kneecap subluxation or dislocation will benefit from a 'do-nut' type brace, which holds the patellar in the groove of the underlying femur while the knee bends and flexes.
These braces will have a 'cut-out' in the middle where the patella lies.
(e) Supports for patellar tendinitis
This kind of brace is generally strap-like and wraps around the knee just in the area over the patellar tendon.
A common brace of this type is the Cho Pat strap.
Other relevant links
Functional brace, Patellar brace, Unloader brace, Infrapatellar brace