Upper Body Strength Training

[Andrea]

The principle of overload is what makes you stronger:
-It's very VERY important to use enough weight to make your sets somewhat difficult. However many reps you do, by the time you get to the last one, you should not be able to complete more than one or two more.
-Using an unstable device of some sort will compromise overload- you can't lift as much, so you aren't going to get as much benefit. This goes for upper/lower body exercise as well as exercises for "core" muscles- you're best off to work them directly with sit ups (weighted, if necessary), good mornings, ab machines, leg lifts, reverse leg lifts, etc. This will make them strongest.
- When you are just starting out, any exercises done in any number of sets/reps will make you stronger, but to continue to see results, you'll have to increase difficulty in some way/shape/form

[Flur]

+1 for yoga. I do Vinyasa Flow (aka Power Yoga). Some teachers give more of a workout than others, so you may need to try a few different teachers to find what you're looking for. I have definitely increased my upper body strength through my practice. When I practice at home sometimes I'll just focus on yoga pushups and arm balances (which require a lot of control and core strength in addition to arm strength). It's also great for stretching out all the muscles that get tight while riding and teaches excellent breath control (which is a huge help when you need to push through on a ride). Not to mention all the mental benefits, getting more in touch with your body, releasing stress, etc...

[Zen]

I'm a big fan of TheraBands.
Anything you can do with a free weight you can do with a TheraBand