Republicans appeared to be picking up governorships from Democrats last night in North Carolina, Rhode Island, West Virginia and Utah, possibly aided by President Reagan's landslide victory at the top of the ticket.

But the Democrats apparently picked up seats previously held by Republicans in North Dakota and Washington. The race in Vermont to succeed retiring Gov. Richard A. Snelling (R) was too close to call.

Democrats controlled 35 of the 50 governors' offices before the balloting, but the election shifted the margin slightly toward the GOP. The last time the Republican Party held a majority of governors' mansions was in 1969, when the GOP had 32.

Of the 13 contested seats, six were held by Democrats -- Arkansas, North Carolina, Rhode Island, West Virginia, Utah and Montana. Seven were held by Republicans -- Delaware, Indiana, Missouri, New Hampshire, North Dakota, Vermont and Washington.

In North Carolina, with nearly 80 percent of the vote counted, Rep. James G. Martin (R) appeared to have defeated Attorney General Rufus Edmisten (D) to fill the seat vacated by James B. Hunt Jr. (D), who was challenging Sen. Jesse Helms (R). Martin associated his campaign closely with Reagan and apparently overtook Edmisten's earlier lead.

In Rhode Island, with vote-counting complete, Edward DiPrete (R), the mayor of Cranston, was victorious over state Treasurer Anthony J. Solomon (D), in the most expensive campaign in that state's history. Democrats have had a lock on the Rhode Island governorship for 42 of the past 52 years, but the GOP made gains in local elections in recent years.

West Virginia's race was extremely close. With 80 percent of the vote counted, networks projected former governor Arch A. Moore Jr. (R) would defeat state House Speaker Clyde M. See Jr. (D).

In Vermont, Attorney General John J. Easton Jr. (R) and former lieutenant governor Madeleine M. Kunin (D) were locked in an extremely close contest with more than three-quarters of the vote counted. If neither gets more than 50 percent of the vote, the Republican-controlled state legislature will decide the contest.

New Hampshire's Gov. John H. Sununu (R) was rolling toward easy victory over state House Minority Leader Chris Spirou (D) in a race dominated by debate over the future of the Seabrook nuclear power plant. Sununu backed speedy completion of Seabrook while Spirou said the state should force cancellation of the project.

With all votes counted in Delaware, Lt. Gov. Mchael N. Castle (R) defeated William T. Quillen (D), a former state Supreme Court justice, for the seat vacated by retiring Gov. Pierre S. du Pont IV. In a year when many other governor races turned bitter, civility and a lack of rancor marked this contest. Both candidates are attorneys and political moderates.

In Arkansas, with almost two-thirds of the vote counted, Gov. Bill Clinton (D) appeared to have soundly defeated Elwood (Woody) Freeman (R), a contractor making his first political race. In 1980, when he was considered a rising star in the Democratic Party, Clinton was defeated for a second two-year term. But he was elected again in 1982 and said that he'd learned to listen to his constituents.

An early victor among the governors was Indiana's Robert D. Orr (R), who defeated state Sen. W. Wayne Townsend (D). Orr, seeking a second term, and Townsend, a hog farmer and 20-year veteran of the state legislature, waged a campaign over issues from state license plates to tax increases.

Orr was reelected despite the state tax increase that he won from the legislature in 1982, the largest in Indiana history.

Auto license plates are part of the Indiana patronage system. The local motor vehicle branches that sell the plates are controlled by the governor's party -- since 1969, the Republicans. Townsend attacked the system in his bid to unseat Orr, hammering at the issue for months and using a television ad that showed mud being splatterd on a license plate. But Orr said it was not an issue and, "I think patronage is a good thing."

Despite the attacks, Orr appeared to be in good shape. Indiana, with a heavy steel and auto work force, was hit hard by the last recession, but unemployment has dropped 6 points, to 7.6 percent, from its high in late 1982.

His campaign took an unusual twist recently with the use of a rock-video campaign commercial targeted at younger voters. Townsend then sent a messenger to the governor's office dressed as singer Boy George.

In Missouri, with 86 percent of the votes counted, John Ashcroft (R), the two-term conservative attorney general, appeared to have triumphed over Lt. Gov. Kenneth J. Rothman (D). They were competing to succeed retiring Gov. Christoper (Kit) Bond (R).

In Montana, Gov. Ted Schwinden (D) was an easy victor in his bid for a second four-year term, network projections showed. Regarded as one of the most popular Montana governors in recent years, Schwinden coopted the Republicans' standard themes with his fiscal conservatism and an economic development program.

Republicans couldn't round up a candidate until late March, when they recruited state Sen. Pat M. Goodover. But Goodover had trouble raising money and putting together a campaign staff, and has been outspent by the incumbent. Republicans haven't won a Montana gubernatorial campaign since 1964.

In neighboring North Dakota, Republican Gov. Allen I. Olson appeared to have suffered defeat at the hands of George Sinner (D), a farmer and state representative, with nearly two thirds of the vote counted. Polls had showed Olson with a big lead in August.

The contest turned bitter. Olson has accused Sinner of supporting the closure of one of the state's two Air Force bases; Sinner said Olson took a remark out of context.

Olson launched an advertising campaign using Sinner's comment, and the challenger fought back with his own advertisement showing a farmer pitching cow manure -- an act he compared to the governor's campaign statements. Charges also were exchanged over Olson's accepting a raise mandated by the legislature after saying he would refuse it.

In Utah, with a third of the vote counted, House Speaker Norman H. Bangerter was in position to become the state's first Republican governor in 20 years in a contest with former representative Wayne Owens (D) to succeed retiring Gov. Scott M. Matheson.

Bangerter's pledge not to raise any taxes during his first two years apparently struck a chord with voters. Owens later went along with a no-tax-increase platform, but would commit himself only to one year. Matheson is leaving a $92 million budget surplus, and while he has been working for Owen, he once said he thought Bangerter would make a pretty good governor.

Washington has been the scene of one of the nation's hottest gubernatorial campaigns. With 40 percent of the vote counted, Gov. John Spellman (R), completing his first term, appeared to have been defeated by by Booth Gardner (D). Gardner is a multimillionaire heir to the Weyerhaeuser timber fortune and is in his first four-year term as Pierce County (Tacoma) executive.

Their race has been described as a contest between "the wimp and the waffle." Gardner is the "wimp," with a voice that has been described as "Elmer Fudd on helium" and a manner that is low-key, painfully shy and unexciting.

Spellman's nickname during his early years as governor was "Waffleman," earned in part by his indecisiveness and in part by a stunt in 1980 when he pulled a waffle out during a primary debate and accused his opponent of "waffling on the issues."

Oct. 25, the Teamsters withdrew their endorsment, saying Spellman had chosen to "viciously attack labor unions" in the campaign.