Nothing trains the core like challenging your stability. A great exercise which challenges your core and balance is the Swiss Ball Rollout. It's very challenging and only requires a Swiss Ball and little space, making it easy to do at home, at the gym, or wherever you please.
1-Start in a kneeling position, with the Swiss Ball in front of you and your forearms resting at a 45 angle on the ball. The Swiss Ball should be placed so that your torso is also at a 45 degree angle.
2-Exhale and begin to roll your forearms over the Swiss Ball, until the ball is almost touching your chest. Keep your core engaged so that your back remains flat, as if in the plank position. Your body should be at the farthest extension without needing to collapse out of form.
3-As you take your next exhalation, roll the ball back to the starting position, ending with your torso in a 45 degree angle to the floor and your forearms resting on the ball. This is one repetition.
Do as many repetitions as you can in 1 minute.