bad, nasty, terrible
She took a bad fall while out riding.

accidental

have, suffer, take
The doctor says she's had a very nasty fall.

break, cushion
Luckily a bush broke his fall.

survive
The chances of surviving a fall under a train are almost nil.

prevent

in a/the fall
He was hurt in a fall at his home yesterday.

fall from
She broke her neck in a fall from a horse.

heavy
light
fresh
a fresh fall of snow

rock, snow (usually snowfall)

fall of
covered by a light fall of volcanic ash

big, dramatic, great, large, marked, massive, significant, substantial
a big fall in house prices
This triggered the recent dramatic falls on the Tokyo stock exchange.

modest, slight, small
steady
rapid, sharp, steep, sudden
unexpected
continuing, further
overall (esp. BrE)
catastrophic

bring, cause, contribute to, lead to, trigger
see, suffer
Share prices suffered a slight fall yesterday.

record, reveal (esp. BrE), show
The opinion polls show a significant fall in her popularity.

report
Both companies reported a fall in profits in the first quarter of this year.

represent (esp. BrE)
This figure represents a fall of 21% on the same period last year.

occur
The fall in age at first marriage occurred during the second half of the 18th century.

fall in
a large fall in share prices

bring about, cause, contribute to, lead to
the actions that led to his eventual fall from power

fall from

the rise and fall of sth
a book charting the rise and fall of the Habsburg Empire

last, this past
the following, next, this, this coming
early, late

weather
color
The trees were on fire with vibrant fall colors.

foliage
New England's gorgeous fall foliage

harvest
equinox
semester, term
He returned to school a month into the fall semester.

heavily
She fell heavily to the ground.

steadily
The rain was falling steadily.

freely
Tears fell freely from her eyes.

limply
Her hands fell limply to her sides.

down, off, overboard
A tile fell off the roof.
He fell overboard in heavy seas.

be about to
let sb/sth
She lifted her arm, but then let it fall.

from
He fell from the fourth floor.

into
One of the kids fell into the river.

on
the snow falling on the fields

onto
Loose bricks were falling down onto the ground.

to
The plate fell to the floor.

almost, nearly
He stumbled and almost fell.

headlong
She fell headlong, with a cry of alarm.

down, over
One of the children fell over.

backwards/backward, forward

be about to
The house looked as if it was about to fall down.

stumble and fall, trip and fall

dramatically, rapidly, sharply, significantly, steeply
The price of coal fell sharply.

slightly
steadily

be expected to, be likely to
Demand is likely to fall by some 15%.

continue to

below
Winter temperatures never fall below 10°C.

by
Expenditure on education fell by 10% last year.

from
The number of people unemployed has fallen from two million to just over one and a half million.

to
Her voice fell to a whisper.

squarely

into
Out of over 400 staff there are just 14 that fall into this category.

outside
That topic falls outside the scope of this thesis.

under
This falls under the heading of scientific research.

within
This case falls squarely within the committee's jurisdiction.

Fall is used with these nouns as the subject:
amount, anniversary, ash, attendance, axe, barometer, blossom, blow, bomb, catch, circulation, cliff, coalition, concentration, confetti, confidence, consumption, cost, count, curl, currency, curtain, darkness, debris, deficit, demand, density, dew, drip, drizzle, drop, dusk, dust, emission, empire, employment, enrolment, expenditure, export, eye, face, fort, fortress, fortune, funding, gaze, government, hail, hair, head, horse, hush, import, incidence, income, index, inflation, investment, leaf, level, light, missile, moonlight, mortality, night, number, odds, output, percentage, population, premium, pressure, price, production, productivity, profit, proportion, rain, rate, rating, receipt, record, regime, rent, reserve, revenue, sale, shadow, share, shell, silence, size, skirt, snow, snowflake, spending, standard, standing, stock, stress, sunlight, supply, support, tax, tear, temperature, tide, total, tourism, tower, trade, tree, turnover, unemployment, value, volume, vote, wage, wall, waterfall, wave, weight, word, workforce

Fall is used with these nouns as the object:
heir, per cent, point, victim