Burpees: If you are unable to fully squat to the floor, and then move back into a plank, you can squat in front of a bench and place your hands on the bench to stabilize yourself as you jump into the plank position.
If you are unable to jump your legs back into the plank you can simply step each foot back into it.
Traditional Pushups: Instead, perform knee pushups or pushups with your hands elevated on the couch, bench, chair, etc.
Prisoner Squats, Jump Squats, In & Out Squats: Instead, perform basic Squat or a squat holding onto a chair.
Prisoner Lunges, Jump Lunges, Front, Side & Back Lunges: Instead, perform a basic lunge holding on to a chair, table, couch, etc. Start with your feet shoulder-width apart, and then step one leg forward. The back leg should be engaged on the ball of the foot, while the front leg should bend down to a 90-degree angle towards the floor.
A major key here is to not let the front knee go forward over the toes, keep it directly above the ankle.
You can do variations of a lunge, including stepping forward or backward into them, stepping up onto a bench, or stepping sideways into side-lunges.
High Knees: Instead, you can modify by doing them at a slow, controlled pace, or simply march in place.
Bicycle Crunches, Six inches, Leg Drops, Flutter Kicks, Laying Knee Raises: Do as many reps as you can with proper form and rest when needed.
Mountain Climbers: Instead, hold on to a chair or couch and perform the exercise, or you can put some towels or paper plates under your feet (depending on the floor surface you are working out on) and instead of jumping your feet back and forth you can slide them.
Jumping Jacks: If your shoulders are injured, or it strains them too much to bring your arms completely above your head, you can modify by only bringing them halfway up, to about shoulder length.