The most common ligament reconstruction that occurs in or around the knee joint relates to the anterior cruciate ligament.
Sometimes, the posterior cruciate ligament can be ruptured and on occasions, it also requires reconstruction.
In addition, there are ligaments on the medial side and lateral side of the knee (the collateral ligaments) which can be disrupted. The need for repair or reconstruction is less frequent but it does exist.
Sometimes, capsular disruptions can occur that may also require repair.
The decision to reconstruct or otherwise depends upon the severity of the injury, the morbidity or discomfort that ensues, the relative instability that persists and the views and advice of your Orthopaedic Surgeon. The level of activity of daily living that you aspire to will also be an indicator. For example, if you intend to spend the remaining years of your life in a chair watching television, a ligament reconstruction is not likely to be required. Conversely, if you want to return to A grade sport at a competitive level, a ligament reconstruction does become more desirable.
These are issues that your Orthopaedic Surgeon will help you understand.