I think David hit the nail on the head - core exercises.
I do running and swimming to keep myself fit which is more for general fitness and the self-defence benefits (able to keep moving and thinking with blood loss/overcome the tiring effects of extreme adrenalin).
I used to do some weights but actually found may aikido getting worse - mainly 'cos I was strengthening my upper body and making myself heavier. Instead I do core exercises such as press-ups (which also exercises stomach) followed by crunches/sit-ups.
Also do plenty of sword cutting (very good to get the body movement), chi gung and some tai chi. Also do an exercise to strengthen the grip and improve finger strength for pressure point strikes; throwing up bricks and catching them with my finge tips.
Now I swim properly I also find this focuses on my core body muscles rather than my arms and shoulders.
My philosophy for training has changed considerably due to time limits (I also have to work!) my main aims are:
- keep fit
- keep fast
- focus on exercises which are related to the movements you want to improve at.
Many weights exercises teach you to isolate your muscles, to keep your body stationary and to use your body ineffeciently - don't bother with them. The only 'weights' I do every so often are pull-ups (strengthen back and shoulders and biceps) and dips (triceps and shoulders) - these utilise your own body weight, for some reason this prevents you getting as bulky as normal weights exercises.