I'm pretty much a cardio addict; I had been running a lot but when it got too cold to run outside I started doing more elliptical, stairclimbing, and treadmill in the gym. I have a harder time with the strength stuff, and my upper body and core are weak so I've been trying for the past few weeks to work on pushups a few times a week and to take some classes at the gym specifically for strength and also abs.
For working abs/core on my own, I do the plank position; I've been working my way up in time and am up to holding it for two minutes at a time. I also use the leg lift machine in the gym where you rest all your weight on your forearms and lift your legs straight up or to the side. I've gotten up to three times of 10 reps each--legs straight up, legs to the left, legs to the right.
I also bought some light wrist weights (I think they're 1.5 lbs each) that I wear occasionally on shorter runs or while stairclimbing; I feel like they've helped me tone my arms a little more.