Sinks: An above-counter vessel sink will sit much higher than an inset below-counter sink, so a vessel should be placed on a lowered cabinet to compensate.
Mirrors: The height of mirrors should be based on your own height. Find an average eye line for everyone using the mirrors and ensure that this height is well within the upper and lower borders of the mirror. 5 feet, 6 inches is average. The bottom edge of the mirror is above the faucet, but allowing the two to visually overlap can create a very elegant effect.
Showers: Shower benches could be a bit lower can typical seat height in order to have a place to perch your leg when shaving. A typical height for showerheads are 6 feet, 6 inches, but can be adjusted if needed. The showerhead should not sit so low that you must crouch, or so high that the water pelts you rather than gently raining down. Shower niches are practical for storage and beauty. In a tub they should be just above the tub surface, but in a shower they should be higher, around 48 inches.
Towel Bars and Hooks: Towels need at least 36 inches typically to hang and robes need 60 inches. A standard towel rail is 48 inches above the floor, but it can be adjusted if needed to line up with something, such as the knob on the shower door.
From Houzz contributer Yanic Simard September 2014, Summarized.