five-mile, etc.
fun, sponsored (esp. BrE)
The school has organized a two-mile fun run for charity.

training
record, record-breaking
The Ethiopian is aiming to produce his second record-breaking run of the week.

go for, have
Let's go for a run before dinner.

go on
I'm going on a fun run tomorrow.

break into
When he saw me he broke into a run.

take
He took a run at the wall and just managed to clear it.

at a run
She took the stairs at a run.

on the run
The prisoners have now been on the run (= escaping by running) for three days.
I usually eat breakfast on the run (= while going somewhere).

make a run for it (= escape by running)

bad, disappointing, disastrous, dismal, poor
excellent, fine, good, remarkable, successful
unbeaten, winning
record-breaking

enjoy, have
Spurs have had a winning run of ten games.

begin
end
Manchester United have finally ended their run of victories.

begin
end

run of
a run of good/bad luck

theatrical (AmE)
long
short
eight-week, six-month, etc.
successful
sell-out

have
The play had a long run in the West End.

begin, end
They play began its run last June.

extend
The show has had its run extended till March.

begin
end

common, general, ordinary, usual
She was very different from the general run of American movie stars.
In the normal run of things the only exercise he gets is climbing in and out of taxis.

against the run of play (BrE)
Villa scored in the 15th minute against the run of play (= although the other team had seemed more likely to score).

print, production
a print run of 20 000

home
play-off, stretch (both AmE)

get, hit, make, play (AmE), score
They've scored another run!
He's only made four home runs all season.

be on, have
Our team is on 90 runs.

allow

defense, game, support (all AmE)

dry, dummy, practice, trial

presidential

run for
Senator Blake's run for the presidency

fast, quickly
John can run very fast.
She ran quickly downstairs.

blindly, headlong
frantically
away, off, out
home
downstairs, upstairs

begin to, start to
get up and, jump up and, turn and, turn to
want to
He just wanted to run away and hide.

down
She turned and ran blindly down the street.

into
He ran headlong into an enemy patrol.

out of
He ran out of the house.

to, towards/toward, up, etc.

efficiently, properly, well
badly
a badly run company

professionally
privately
jointly
The school is jointly run with the local parish.

independently
The group is run independently of college authorities.

try to
Stop trying to run my life for me.

manage to
help (to), help sb (to)

efficiently, smoothly
The engine was running very smoothly.

continuously

on
Our car only runs on unleaded.

be up and running
We soon had the sound system up and running.

smoothly
Things ran very smoothly for a while.

concurrently, consecutively, simultaneously
He was given two twelve-month sentences to run concurrently.

in parallel, in tandem
The two experiments run in parallel.

regularly
Local buses run regularly to and from the school.

late
The train was running late, as usual.

between, from, to

successfully, unsuccessfully
He ran unsuccessfully for the Senate in New York.

for
He hopes to run for president in 2016.

Run is used with these nouns as the subject:
application, argument, blood, bus, cable, chip, college, colour, computer, course, crack, ditch, dog, electricity, engine, exhibit, exhibition, eye, ferry, footpath, footstep, generator, horse, hound, lane, lease, ledge, line, machine, magazine, make-up, mascara, meter, motor, mouse, murmur, nerve, nose, path, pipe, power, program, railway, reactor, river, road, route, scar, sentiment, servant, shiver, shower, software, spider, stream, street, stripe, system, tap, taste, term, tide, trail, train, tram, tremor, trust, tunnel, volunteer, water, wire, worker, year

Run is used with these nouns as the object:
ad, advert, advertisement, affair, airline, appliance, application, article, ball, bar, bath, blockade, blog, boutique, brothel, brush, business, cable, cafe, campaign, candidate, car, charity, check, class, clinic, club, column, comb, command, commercial, company, computer, contest, country, course, crèche, danger, deficit, department, desk, dishwasher, division, economy, editorial, election, empire, engine, enterprise, errand, estate, excerpt, excursion, experiment, factory, farm, feature, festival, fever, finance, finger, fingernail, firm, franchise, fund, gamut, garage, government, group, hand, headline, home, hotel, hotline, household, inn, lap, length, lottery, machine, marathon, meeting, mile, mill, mine, ministry, mission, museum, network, newspaper, office, operation, palm, pipe, plant, play, playgroup, poll, practice, prison, program, programme, project, racket, raffle, railway, reactor, relay, restaurant, risk, scan, scheme, school, search, seminar, service, session, shop, simulation, site, software, stall, station, store, story, surplus, syndicate, system, tap, team, temperature, test, thing, tongue, train, trust, washing machine, website, wire, workshop