Does it matter what I put in a dwarf's bedroom, except for the bed? I've heard they can use cabinets and coffers. What should I make sure to put in their bedrooms if I want to take good care of my dwarves?
You should at least build a cabinet and a door (separating the room from the outside).
They have the following uses:
Cabinets help with preventing random pieces of clothing lying around the fort and surrounding area. Dwarves will claim new clothing as the old one becomes broken, but they often don't but it on immediately, and even if they do they leave the old piece just lying there where they changed. If they have a cabinet in their room, however, they'll try to store it inside. A cabinet holds somewhere around 10 pieces of clothing, so for married couples sharing a single room, you'll likely want to put two of them inside.
Doors are as much part of a "proper" room as a bed is, but they also have other important roles. One, they stop floods, so in case of accidental flooding with water or magma, some of your Dwarves might actually survive if they were in their rooms. Second, they act as obstacles to invaders just freely roaming through your Dwarves' bedrooms. Third, you can set them to "forbidden", separating the Dwarf from the rest of the fort - very useful with a vampire suspect or other troublesome subjects.
The one other item often used, but not strictly necessary in bedrooms are coffers. They act like cabinets in that Dwarves can store their non-clothing items in them, but Dwarves seldom own any items which they aren't also holding on to as they mill around the fort.
Other pieces of furniture (armour and weapon stands, statues, chairs and tables, windows, floor grates to the sewers for flood control, floodgates for noble termination and so on) are purely optional, unless the room belongs to someone of power and they request it.
(Applies to version 0.34.11)