big, huge, large
small, tiny
built-in
walk-in
broom, coat, linen
bedroom, hall, hallway
storage, supply

close, open
lock
raid, rummage through, search
I raided Bob's closet for something to wear.
He searched his closet for something to wear.

clean, clean out, organize
fill

be filled with sth, hold sth
Her closet was filled with black clothes.

door
space
Do you have much closet space in your new house?

in the closet
clothes hanging in the closet

from the closet
I picked a shirt from the closet.

to the closet
He went to the closet and pulled out a suit.

be in the closet, stay in the closet (= refuse to say publicly that you are gay)
come out of the closet (= say publicly that you are gay)
More public figures are finding the courage to come out of the closet.

a skeleton in the/sb's closet (= something shocking in your past)
They were hoping to find some skeletons in his closet.

Closet is used with these nouns:
homosexual, lesbian