Most people only think of abdominals when strengthening their core, but an equally important area is your back. I have free hand weights at home and I use the heaviest ones and lean over with the weights in front hanging and stand up keep them close to the body - this strengthens the lower back. Only do this if you don't have problems. Strengthening your upper back improves posture and helps the abdominals.

You can also go on your knees with hands on the floor like a cat or dog - extend the your arm straight out and the opposite leg - you can feel the core helping you balance...then alternate several times.

The bicycle move is also good for abdominals - lay on your back and raise and move legs as if riding a bicycle - I put my hands under my backside for support. Do a variation of the sit up but this is a more advanced sit up - roll your body a little side ways with legs slightly bent and do sit ups - this strengthen the side abdominals.

If you sit at a desk to do computer work - you could use a big balancing ball. This forcing proper posture and balancing for the core. I saw one elementary school had the kids use these instead of chairs. There was less figeting and noise. Good luck.