What exercise routine can I do if my knee has little or no remaining cartilage?

Non-loading. At 42 and with a history of arthitis, you want to minimize the load across the knee joint. You want to focus on keeping your quad strong. The best excercises are: swimming, biking, leg press, wall sits, hamstring curls, and possible eliptical. Avoid stair climbers and any type of leg extension. Avoid lunges and plyometric excersices as well. Try taking glucosamine suppliments suchas osteobiflex.
Stationary Bike. Best exercises would be ones that allow you to move your knee without any significant weight/load across the joint. Examples are: stationary bike set to low resistance or pool exercises.