I figured I'd start a conversation here about the development of US politics without Watergate. I think one of the biggest changes would be a great change in the power dynamics of the Republican party. Nixon and his supporters would likely maintain control of the party for long periods of time.
Nixon 1968-1976
Without Watergate Nixon goes through both of his terms retaining his massive popularity.
Agnew 1976-1980
With Agnew's policies differing greatly from Nixon's own Nixon does not endorse his former VP at first, thus leaving the primaries relatively open. A close three way race soon emerges between the VP, Governor Ronald Reagen, and Senate Minority Leader Howard Baker.
Finally at the convention with Baker having been knocked out with the least votes and a new ballot preparing to be cast Nixon endorses his former VP. This is enough to put Agnew over the top and he captures the nomination and, with Baker as his VP, wins the presidency over Jimmy Carter.
Jimmy Carter 1980-1988
In the 1980 primaries Reagen again challenges Agnew for the nomination of the Republican Party. Reagen wins more states and beats Agnew in term of combined popular vote but Agnew captures the most delegates and takes the nomination.
In response Reagen supporters form the new National Conservative Party and draft Reagen as their candidate. Jimmy Carter is again nominated by the Democrats and, facing a divided opposition, wins the presidency easily.
In 1984 the Right remains divided between Reagen for the National Conservatives and, this time, Senator George Bush for the Republicans. Jimmy Carter wins reelection.
Walter Mondale 1988-1996
In the 1988 election the Republicans seem nearly dead and National Conservative, former VP Howard Baker nearly defeats current VP Walter Mondale for the presidency. Yet Mondale narrowly wins.
As 1992 approaches it looks as though the National Conservatives could win the presidency for the first time. Then famous businessman Ross Perot stuns the nation by throwing his hat in the ring as a Republican, winning the nomination. The newly re-defined Republicans win a good amount of votes allowing Mondale to win reelection.
Mario Cuomo 1996-2004
In 1996 Perot again leads the charge for the Republicans, giving the Democrats the major advantage once again. Long time popular governor of New York Mario Cuomo captures the Democratic nomination and wins the election by a large margin.
In 2000 the Republicans again begin to fade off as the National Conservatives take control of the right. Yet Mario Cuomo remains a popular president and narrowly wins reelection.
Newt Gingrich 2004-Present
In 1994 Newt Gingrich took the lead of the Contract with America that lead to the National Conservatives gaining some 40% of the legislature. He lead the campaign to form a coalition between the right and in 1998 he succeeded and became speaker of the house. He continued in this role until the 2004 election.
By 2004 the Republicans had finally faded into oblivion and the National Conservatives had won the long struggle for the right. Thanks to this Gingrich defeated Governor of New York and son of the current president, Andrew Cumo, ending 24 years of Democratic control of the presidency.