Pushups are really good for general upper body strength. They target chest, abs, front shoulders, and triceps. Start on your knees if you can't do it from a plank position. Keep building reps until you can do a regular set of 12 pushups. Try to do 5 sets.

Pullups. You don't need a pull-up bar, just a wood or tile floor. Lay down flat with your arms in front of you on the floor. Pull your body with your arms and hands. Then, push yourself back to the start position. Strengthens
shoulders, back, biceps. Do maximum reps 5 times.

Weighted unbalanced squats. Hold 5 pounds above your head with one arm, holding 10 pounds in the other arm in your hand hanging down in a natural position. Keep posture upright. Don't lean forward at waist. Do 12 squats. Switch arms up/down and do another set. Strengthens shoulders, lower back, and abs (stability is key to this exercise), plus quads and gluts.

Bent over rows will target upper back.

Good point, PP, about using body weight exercises. Even lunges, holding a dictionary or large dumbbell above your head.

Don't need machines for upper body work. Get some dumbbells in 5-12 pound range. Get a strength training book or print some plans off the internet. Assuming you're a woman, I've heard good things about these books: New Rules of Lifting for Women and Strong Women Stay Young.

Also, push-ups and triceps dips are great for upper body work. You can do them anywhere, anytime without equipment.

For women in particular, strength training is more and more important as you get older.

P.S. Not a body builder, just want to stay in reasonable shape.

I'm close to 60. I run some during the week for cardio. I used to be at a gym for circuit-training/upper body work but let that membership lapse as it's a bit of a trek to get to.

Not really interested in joining a gym again, but I'd like to do some more upper-body at home. I'm thinking of getting some free-weights but I'd need guidance on the weights and technique. Where can I go for this? Or should I get an (inexpensive) machine?