These are the more common ligament problems in the knee:
Sprained cruciate ligament
Instability of the knee can follow an incident where the cruciate ligament is partially, but not completely, torn.
Torn cruciate ligament
Usually a dramatic event during a sporting activity. Loud noise of a 'pop', and pain, and a sudden feeling of instability of the knee. Most often the anterior cruciate ligament, which is more serious than a posterior cruciate ligament tear.
Sprained collateral ligament
Injury may lead to a sprain, or partial tear, of the ligaments on the side of the knee, usually the inner one (medial collateral). This leads to pain over the tear and maybe some bruising.
Torn collateral ligament
Total break of the collateral ligament. Leads to pain over the ligament and also a feeling of instability.
There are other smaller ligaments in the knee. These may also suffer tears and diagnosis may be more subtle and difficult.