high, tall
low
barbed-wire, chain-link, iron, mesh, metal, picket, rail (esp. AmE), steel, stone (AmE), wire, wood (AmE), wooden, wrought-iron
The house was surrounded by a white picket fence.

electric, electrified (AmE)
back, backyard (AmE), garden
border (esp. AmE), boundary, perimeter, security
the airport perimeter fence

invisible (= to keep pets in)
left-field, outfield, right-field (all in baseball)
privacy (AmE)
She walked over to the tall wooden privacy fence.

political (figurative)
a proposal approved by people on both sides of the political fence

build, erect, put up
climb, climb over, hop (AmE), hop over (esp. AmE), jump, jump over, scale
mend (figurative)
The White House already is struggling to mend fences with Europe.

post
line (esp. AmE)
the fence line separating the United States from Mexico

over a/the fence
She leaned over the fence.

fence around, fence round (esp. BrE)
a fence around the site

Fence is used with these nouns as the object:
yard