A look at some of the offices and issues at stake:
Businessman Matt Bevin becomes only the second Republican in four decades to win the governor's seat in Kentucky, defeating the Democratic attorney general in a race that acted as something of a referendum on health care and gay marriage.
He will succeed Democratic Gov. Steve Beshear, who is termed out of office.
Bevin describes himself as a Christian conservative and defended Kim Davis, the county clerk who was jailed for refusing to issue marriage licenses to same-sex couples.
He opposed the state's expansion of Medicaid, the government health insurance program for lower-income people, which was made possible by President Barack Obama's health care overhaul. Bevin wants to replace it with a health care plan requiring more money from participants.
His Democratic opponent, Jack Conway, supported the Medicaid expansion. As attorney general, Conway also opted not to appeal when a federal judge ordered Kentucky to recognize same-sex marriage, a year before the U.S. Supreme Court legalized it nationwide.
In Tuesday's only other gubernatorial race, Republican Mississippi Gov. Phil Bryant won re-election to a second term after spending $2.7 million in his campaign against Democrat Robert Gray, a truck driver who spent just $3,000.
Just three states had general legislative elections Tuesday, although at least 10 others held special elections to fill vacant seats.
The biggest battle was for control of the Virginia Senate, where Republicans held off an attempt by Democrats to win a majority and maintained their 21-19 edge. A gain of just one seat by Democrats could have flipped control because Democratic Lt. Gov. Ralph Northam would serve as the tiebreaker.
The Senate races were expected to be among the most expensive in Virginia's history, with candidates and outside groups spending more than $10 million and running more than 20,000 TV ads.
Republicans were expected to maintain majorities in the Virginia House and in Mississippi's two chambers, while Democrats held on to their majority in the New Jersey Assembly and actually picked up a seat.
In Michigan, former state Reps. Todd Courser and Cindy Gamrat lost bids to regain their old seats, just months after they left office following revelations they had an extramarital affair and concocted a strange story to make the truth seem less believable.
More than 300 cities held mayoral elections, including the nation's fourth and fifth largest cities of Houston and Philadelphia.
In Houston's nonpartisan election, seven candidates campaigned to succeed term-limited Mayor Annise Parker, with two moving on to a Dec. 12 runoff. State Rep. Sylvester Turner, the top vote-getter, will face businessman Bill King.
In Philadelphia, where Democrats hold a 7-to-1 voter registration edge over Republicans, Democrat Jim Kenney, a former city councilman, defeated a Republican business executive to succeed term-limited Mayor Michael Nutter. Kenney had pledged to step up the fight on poverty and provide universal pre-kindergarten.
Other large cities holding mayoral elections included San Francisco and Indianapolis, Columbus, Ohio, and Charlotte, North Carolina.
In Salt Lake City, two-term incumbent Mayor Ralph Becker faced a challenge from former state lawmaker Jackie Biskupski, who would become the city's first openly gay mayor if elected. The Salt Lake County clerk said a crush of mail-in ballots was dropped off at polling places and other voting centers Tuesday, potentially delaying a final result.
Democrats won all three open seats on the Pennsylvania Supreme Court, a race that attracted at least $11.5 million in campaign contributions.
Democrats now lock in a majority for at least the next 10 years. That potentially could influence the next round of legislative and congressional redistricting in an important swing state.
Ohio voters rejected a ballot initiative that would have legalized recreational use by adults 21 and older and allowed for medicinal use by others. The initiative would have authorized 10 particular facilities to grow marijuana. A separate measure, referred to the ballot by legislators, sought to nullify the marijuana proposal by adopting a ban on constitutional amendments that create an economic monopoly.
Colorado voters, who approved the recreational use of marijuana in 2012, decided to let the state keep $66 million in marijuana tax revenue to be spent on schools and other projects. A Colorado law requires new tax revenue to be refunded when overall state income exceeds projections.
Houston voters rejected a city ordinance that sought to provide non-discrimination protections for gay and transgender people. The City Council approved the ordinance in May 2014, but a legal challenge led to Tuesday's ballot question. Opponents included a coalition of conservative pastors who said it infringed on their religious beliefs against homosexuality. With same-sex marriage now legal nationwide, nondiscrimination laws have become the new priority for many lesbian, gay, bisexual and transgender groups.
San Francisco voters were deciding whether to limit the "sharing economy" services in which people rent rooms directly from others through Internet bookings. A ballot measure would cap short-term housing rentals at 75 days a year and require Internet hosting companies such as San Francisco-based Airbnb to pull listings that violate the limit. Airbnb has poured millions of dollars into the opposition campaign.
A separate San Francisco ballot measure proposed a $310 million bond issue for affordable housing. In Maine, voters approved a $15 million bond issue for housing for low-income seniors.
Texas voters approved a constitutional amendment that is expected to raise about $2.5 billion a year for road and highway improvements starting in 2017. The measure will divert general and vehicle sales tax revenue toward a highway fund when collections exceed certain thresholds. Additional money will become available in 2019, if tax revenue from vehicle sales and rentals exceeds a certain threshold.
The passage comes just one year after Texas voters approved an amendment diverting $1.7 billion of oil and gas tax revenue from the state rainy day fund to highways.
Maine voters passed an $85 million bond issue for roads, bridges and other modes of transportation. It is projected to draw more than $120 million in additional federal funding.
In Mississippi, voters were choosing between two rival education measures, or opting for neither. A citizens' initiative would require "an adequate and efficient" public school system and grant the courts power to enforce that. An alternative, referred to the ballot by legislators, would simply require the Legislature to provide an "effective" school system. The measures come as state funding for schools has fallen short of what is called for under state law, but neither measure would specifically raise taxes.
A Washington ballot initiative backed by Microsoft co-founder Paul Allen and various animal-rights groups would make it a state crime to buy, sell or trade products coming from certain wild animals. The ban targets endangered species of elephants, rhinoceroses, tigers, lions, leopards, cheetahs, pangolins, marine turtles, sharks and rays. In Texas, voters approved a ballot measure that creates a constitutional right for people to hunt, fish and "harvest wildlife."