The longer I work in fitness training the more I see people who have been really injured as a result of poor exercise choices. What makes it worse is that often these exercises were chosen by a paid personal trainer!
What do I mean when I say poor exercise choices?
First, there are some exercises that in general cause more harm than good. These include the seated leg press, the seated leg extension, the hamstring curl, the seated ab/adduction machine, the overhead shoulder press, and spinning. None of these mimics any good movement patterns for daily life and all can make existing injuries worse.
Second, instability does not always equal core strengthening! If you can barely stand on one leg for any period of time why get on a Bosu and try bicep curls on one leg? I can guarantee you will be no better for that exercise.
Third, flexibility is not always appropriate. Stretching your lower back all the time will in fact overstretch your lumbar support muscles and make you more prone to back injury. You want to use stretching judiciously.
Basically, the best exercises are the simplest. Squats, lunges, planking, side planking, bridging, and pushups are all great and you need no equipment.