I always check and balance wooden props. everything else it really just depends.
gws thin electric props, I see no point in balancing. I occasionally check my apc props, but most of my motors rarely get over 5000rpm's when flying. my trike planes do not eat up props like my convential gear planes can, so they last much longer and I generally do balance them. when I was flying my slow stick, with the stock wire gear and a 2200mah battery, I almost always eat at least one prop per outing unless I stay on grass. but I like to fly really low and keep doing touch and goes. your mileage will vary.
tires can weigh several hundred pounds when they are spinning. even so, tire balancing is more of a static balance then actually accurately stopping vibration. tires themselves do not start to take shape until they are in the 100 mph range. as most cars never see these speeds, they do fine.
semi truck tires can weigh over 500lbs a peice, and they only balance the steer tires to keep the vibration out of the steering wheel.