What cadence should I aim for? I recently got a cyclocomputer that measures cadence and I'm not sure what a good speed is or what benefit I would get by altering my natural cadence.  On good, level tarmac, I find myself doing about 75-80 RPM.  I'll get North of 100 when sprinting away from a stoplight, and down in the 50-60 range when mounting a moderate incline.

I don't know what might impact cadence, but I'm 5'11 (180 centimeters), 150 pounds (68 kilograms, 10.7 stone).  In addition to biking 30-40 miles a week, I do CrossFit, a combination of gymnastic and weightlifting exercises, so I've got quite a bit of raw strength.
For any given speed, you can either spin at a higher cadence in a lower gear, or a lower cadence in a higher gear.  The high cadence + low gear combination should reduce the strain on your joints since you don't have to push as hard.  You just have to do it more often.

I like to ride around 90rpm and sometimes drift up to 100-110 especially if I'm trying to catch up to or overtake someone.  I'll drop down to 80 for long, steep climbs (seated -- no idea what my cadence is standing).

Lance Armstrong apparently maintains 110rpm for efficiency.  It took me a while to get used to 90 so I'd suggest building up to it slowly.  Let us know when you can do 110 comfortably!