Three incumbent governors seeking new terms and two House members trying to move up the political ladder face tough contests today in the biggest primary day of this election year.

For the most part, though, gubernatorial and congressional incumbents look like safe bets as voters in 13 states choose party nominees.

Gov. Hugh Carey of New York and his colleague next door in Connecticut, Gov. Ella Grasso, are both being challenged by their lieutenant governors in Democratic primaries. In Wisconsin, Gov. Martin Schreiber has had a lively battle with businessman David Carley for the Democratic guvernatorial nomination.

Rep. Donald Fraser, a liberal Democrat who gave up a safe spot in the House to seek a Senate seat, has a tough fight in a Minnesota primary against trucking and baseball magnate Bob Short. Across the line in Wisconsin, Rep. Bob Kasten, a conservative Republican who also left a safe House seat, seems to have at best an eve chance in his campaign for the bubernatorial nomination.

Here are state-by-state highlights:

New York - Carey faces strong challenges from two old friends: Lt. Gov. Mary Ann Krupsak, Carey's running mate in 1974, and state Sen. Jeremiah Bloom, who represents Carey's native Brooklyn. Both Democrats have charged the governor with ineffectiveness and a general lack of interest in his job. Although the challenges are embarrassing to Carey, he is favored to win renomination.

Rep. Frederick Richmond, the Brooklyn Democrat who admitted to Washington police that he made sexual advances toward a male teen-ager, has a close primary battle with Bernard Gifford, who has made Richmond's sexual misdeed a campaign issue.

Connecticut - Grasso seems to have weathered some trouble earlier this year and is now favored to win nomination over her lieutenant governor, Robert Killian. Rep. Ronald Sarasin is unopposed for the GOP gubernatorial nomination.

Rhode Island - Sen. Claiborne Pell seems sure to win renomination over two challengers in the Democratic primary. Baking executive James G. Reynolds has no opposition for the GOP Senate nomination. The hot race here is for mayor of Providence; Republican incumbent Vincent Cianci, recently accused by New Times Magazine of committing a brutal rape in 1966, faces a strong challenge.

Vermont - Republican Gov. Richard Snelling and Republican Rep. James Jeffords are unopposed for renomination. There are contests for both jobs on the Democratic side, but Jeffords and Snelling are strong favorites in November no matter who challenges them.

New Hampshire - Gov. Meldrim Thomson, a Republican, and Sen. Thomas McIntyre, a Democrat, should both win renomination. But the flamboyant Thomson has a well-known primary challenger - former governor Wesley Powell. Powell has indicated he will run as an independent in November if Thomson takes the GOP nomination today.

Florida - Democrats have a seven-way scramble for the race to succeed retiring Gov. Reubin Askew, and two Republican seek that nomination. Reps. Sam Gibbons, a Democrat, J. Herbert Burke, a Republican, both face spirited primary challenges.

Minnesota - Fraser had expected smooth sailing in the primary for the Senate seat that belonged to the late Hubert Humphrey, but he ran into a conservative buzzsaw in Short, who has made the Democratic primary a close one. Sen. Wendell Anderson also has a Democratic primary challenger, but seems a likely winner today. Republicans have hard-fought races for both Senate seats - even Harold Stassen is in the running to challenge Anderson.

Wisconsin - Schreiber, the lieutenant governor who moved up last year when Gov. Patrick Lucey was made an ambassador, has had a tough primary fight with Carley, a millionaire boasting excellent Democratic credentials. In the GOP race, Kasten was an early favorite but has apparently been caught by educator Lee Dreyfus.

Arizona - Voters have reacted with yawns to gubernatorial primaries in which incumbent Bruce Babbitt is expected to take the Democratic nomination and three Republicans are in tight race to challenge him.

Colorado - Sen. Floyd Haskell has no Democratic opposition in his race for a second term. Republicans consider Haskell highly vulnerable in November, and Rep. William Armstrong will probably beat astronaut Jack Swigert today for the right to take him on. Two conservative state senators are in a close race for the GOP nomination to challenge Gov. Richard Lamm, who is unopposed in the Democratic primary.

Nevada - Seven Democrats and three Republicans are battling for the race to succeed retiring Gov. Mike O'Callaghan. Lt. Gov. Robert Rose is favored on the Democratic side, and Attorney General Robert List among Republicans.

Utah - Two Democrats are seeking the nomination to challenge Republican Rep. Dan Marriott, who is running for a second term.

Wyoming - Two wealthy legislators are competing for the Republican nomination to challenge Gov. Ed Herschler, who has no opposition in the Democratic primary. Both parties have active primary races for the open Senate and at-large House seats. Notable here is the maiden political campaign of Gerald Ford's White House chief of staff, Richard Cheney, who is seeking the GOP House nomination.