checkout (AmE), post office (BrE), shop (esp. BrE), store (AmE)
There was a line of people waiting at the checkout counter.

cosmetic (AmE), cosmetics, make-up
deli, delicatessen, meat
He works at the meat counter.

bar, lunch (AmE)
They sat on high stools at the bar counter.

check-in (AmE), reception, ticket (esp. AmE)
an airline check-in counter

bathroom (AmE), kitchen (esp. AmE), sink (AmE)
She put her bags down on the kitchen counter.

Formica™ (esp. AmE), glass, granite, marble, wooden

serve at (esp. AmE), serve behind (esp. BrE), work at (esp. AmE), work behind
Mary worked behind the counter at Bacon's for a few hours a week.

wipe, wipe down
The bartender wiped down the counter in silence.

approach
He approached the counter and showed his ticket.

top (esp. AmE)
The kitchen had black marble counter tops.

staff (BrE)
post office counter staff

across a/the counter
He pushed the money across the counter to her.

at a/the counter, behind a/the counter
The assistant behind the counter gave a curt nod.

on a/the counter
all the goods on the counter

over the counter (often figurative)
She handed me my coffee over the counter.
This kind of medication cannot be bought over the counter (= without a prescription).

effective

counter to
an effective counter to the blandness of modern culture