big, huge, major, massive
lengthy, long, long-running, ongoing, sustained (esp. BrE)
effective, successful
unsuccessful
aggressive, determined, intensive, strong, vigorous
bitter, fierce, vicious
concerted, orchestrated
a carefully orchestrated campaign against striking workers

joint
official, public
international, local, national, nationwide, worldwide
one-man (esp. BrE), one-woman (esp. BrE), personal
She has fought a one-woman campaign for ten years about the lack of childcare provision in the town.

grass-roots
They began a grass-roots campaign to encourage people to shop locally.

congressional (AmE), election, electoral, gubernatorial (AmE), leadership (esp. BrE), political, presidential, primary (AmE), re-election, referendum (esp. BrE)
Conservative, Democratic, Labour, Republican, etc.
ad (informal), advertising, branding (esp. AmE), marketing, promotional, sales
PR, propaganda, publicity, public relations
media, poster, press (esp. BrE), print (esp. AmE), television, TV
anti-corruption, anti-drug, anti-smoking, etc.
protest
awareness
a health awareness campaign to promote a healthy lifestyle

lobbying
fund-raising
letter-writing
Local people started a petition and letter-writing campaign to keep the hospital open.

literacy
recruitment
air, bombing, guerrilla, military
the terrorists' bombing campaign

hate, terror, terrorist
dirty tricks (esp. BrE), disinformation, smear, whispering
Her political opponents ran a whispering campaign against her.

begin, initiate, launch, mount, start, unveil
The company launched a huge advertising campaign.

conduct, execute, fight, run, undertake, wage
People have criticized the way in which she conducted her election campaign.

coordinate, manage, orchestrate, organize, plan
lead, spearhead
She led a successful campaign against the closure of the library.

create, design
We designed an Internet marketing campaign.

join, support, take part in
finance, fund, sponsor
The anti-fur organization financed an ad campaign featuring celebrities.

intensify, step up
The government has intensified the military campaign against the rebels.

begin, get underway, start
The general election campaign gets underway today.

unfold
be aimed at sb/sth, focus on sb/sth, target sb/sth
a concerted campaign aimed at educating young people about the dangers of drugs

aim to do sth, be designed to do sth
The campaign aims to inform the public of the dangers of this disease.

call for sth, demand sth
feature sb/sth
The campaign featured athletes talking about healthy lifestyles.

advertise sth, tout sth (esp. AmE)
fail, succeed
The campaign failed to achieve its objectives.

aide (esp. AmE), manager, staffer (esp. AmE), strategist, team
strategy
headquarters
A news conference was held at the party's campaign headquarters.

issue
Education has become an important campaign issue.

promise
The President kept his campaign promises.

slogan
ad, commercial (both esp. AmE)
A Republican campaign ad alleged he was soft on crime.

contributions, donations, finance, financing
regulations governing political campaign financing

contributor (esp. AmE)
trail
election candidates on the campaign trail(= going around the country campaigning)

during a/the campaign
They met regularly during the campaign.

campaign against
a fierce campaign against hunting

campaign by
the political campaign by the Republicans

campaign for
the campaign for racial equality

a campaign of disobedience, misinformation, vilification, etc.
A campaign of intimidation was waged against people trying to vote.

a plan of campaign (esp. BrE)
After sliding in the opinion polls, the party had to rethink its plan of campaign.

actively, aggressively, hard, heavily (esp. AmE), strongly (esp. BrE), tirelessly, vigorously
We will campaign hard for an end to the ivory trade.

effectively, successfully
Local people have successfully campaigned against the building.

openly, publicly

against
Local communities are campaigning against the dumping of toxic waste.

for
We have campaigned for better conditions.

on
The group campaigns on a range of environmental issues.

on behalf of
We campaign on behalf of consumers.