My all time favorite true body strength and core exercises are PLANK and PUSHUPS
Hold Plank for 30-60 seconds, whip out 10-15 Pushups and repeat for 3 sets.
How to do Plank
1. Lie face down resting on the forearms,palms on the floor.
2. Push off the floor, raising up onto your knees(beg. level), or on your toes(advanced level).
3. Keep your back flat, in a straight line from head to heals.
4. Contract your abdominal and don't let your back sag or your rear end pike.
Pushups can be done on your knees or up on your toes.