It depends.
Viet Nam.
Could go either way. There is strong evidence JFK was reconsidering his involvement in the Viet Nam War because he explicitly remembered what happened to the French. LBJ basically thought he was was doing what JFK wanted, but LBJ & JFK were never close.
I believe it was an Atlantic Monthly piece.
Civil Rights.
It took heavy pressure from MLK on LBJ to get moving on this front, and a worsening situation across the United States. If JFK lives any civil rights legislation will not be as sweeping as OTL legislation.
The 1964 Election.
JFK will defeat Goldwater (though you can actually mount a decent case for a close election, and an unlikely though possible upset). The key thing is that JFK & Goldwater had agreed to a series of debates focused on policy—this will cement the debate (and possibly cement meaningful debates, not OTL's garbage) in the American political lexicon as of then, not 1976 IOTL. Butterflies may make it possible for Rockefeller to win the Republican nomination as well, but he would probably still lose to JFK.
Liberalism.
No Great Society to show the limits of government intervention and probably no entitlements means the US's budget situation will be far better off in the future. Thus government intervention and being a liberal will be acceptable for the foreseeable future.
Conservatism.
Without the stinging defeat of Goldwater in what conservative activists considered an unfair fashion (i.e. the Daisy Ad, bomb the Kremlin, etc… which were outgrowths of LBJ's desire to win an overwhelming victory no matter what) modern political conservatism may look different. Butterflies may kill the supply-siders, and regardless no Watergate means the Republican establishment will retain enough power to rein in the excesses of the neoconservative/supply-siders/southern religious voters.
The 1968 Election.
No RFK of course and probably no McCarthy, and LBJ is getting older and sicker so I'm not sure he is willing to run if he wasn't already President. That leaves Humphrey and a few others: perhaps Scoop Jackson,
The Future.
Ronald Reagan will almost certainly be a prominent player, and may take the 1968 nomination and (even) win. Arguably this would be a good thing: Ronald Reagan when he still believed in the traditional Republican balanced budgets and in an era when higher military spending was affordable (if there is no/limited Viet Nam War).
RFK is bound to be a major voice in the United States Senate if he chooses to run for it, and may run for President a few cycles in the future. Alternatively he may choose to go for Governor of New York (which would be pretty interesting, I think). Alternatively (even more so) he may end up doing something entirely unexpected.
EMK (Teddy Kennedy) will not watch the lonely retreat from liberal politics that he had to IOTL, and will probably become Majority Leader of the Senate at some point (RFK wasn't interested in that kind of detail).
JFK is going to be the elder statesmen of a still liberal Democratic power. Speculation as to what he'd do afterwards is varied but my favourite is him buying a newspaper (presumably the Boston
Globe) and seeking to make it into a great paper. Alternatively he may run again for the Senate (though the Kennedy's had a long tradition of not challenging the "Republican" seat in Mass.) or head a university.
Nixon may mount a comeback, but butterflies probably leave Rockefeller in healthy shape in a somewhat different Republican Party and with a less stunningly defeated Goldwater Reagan too probably looks pretty good in 1968 and thus Nixon is squeezed out.
MLK will live (barring getting assassinated despite butterflies), and in combination with either a Reagan more concerned about cities (due to earlier elections, and the need to keep the Rockefeller Republican northern base) or with a liberal President blacks may avoid the deadly spiral of school bussing draining the property tax base—and hence the school tax base—of the inner cities.
Anyway… who really know. The original view was that JFK would have made everything better. The current view is that JFK would have come off looking badly, and things wouldn't have turned out that much better. The revisionist view (outlined above) is that JFK did not equal magic, but that he had a solid chance of taking the US to a better place than in went IOTL.
One key is whether or not (as speculated by Zabel & Turtledove in
The Impeachment of JFK) the "gentleman's agreement" between the presidency and the press over his infidelity (and concealment of his illness) is broken out. If done while in office it will get messy, but post-presidency JFK will probably be fine if a little tarnished.
Previous threads:
JFK Assassination Failure
What if John Kennedy was never Assassinated?
JFK Lives
JFK is not shot. Serves two full terms.
What if JFK was not assassinated?
Kennedy's Legacy
DBWI: Kennedy Assassinated 1963
The Mother of all What Ifs (JFK Lives)