They have not all been JFKs, you know - marching in boldly to the strains of 'The Boys of Wexford' and exiting to the plaintive choruses of 'Toora Loora Loora' - while the Irish public wiped their tears of pride.
US president John Fitzgerald Kennedy's magic visit in 1963 was a tee-totally genuine one-off national experience, replete with mutual warmth, affection and respect. It was, quite simply, a homecoming for him and a milestone in opening a new era of Irish self-confidence.
But it also happened in an age of considerable Irish and US political innocence. And months after it happened, the visit's piquancy was heightened by being viewed through a lens of sorrow and shock at his brutal murder.
Since then, the serving US presidents visiting "the auld sod" have engendered mixed feelings here. Let's count them off and invoke some memories.
There was Richard Nixon in October 1970, looking up his Irish Quaker roots in Timahoe, Co Kildare, and also visiting his wife Pat's forebears' home place in Co Mayo. It was the height of the Vietnam war and there were anti-war demonstrations in Dublin, with his motorcade being pelted with eggs.
This writer recalls exchanging greetings with Nixon on the Tipperary Road outside Limerick city, or so it seemed for a brief moment, as I waved and he waved just after that. Mind you, the poshies have long since been disabusing me of that one with their "correlation does not imply causation" guff - but let's not digress too much here.
Point is that Nixon's visit is now dubbed the "forgotten visit". Unlike JFK, Irish recall might be through the lens of Tricky Dicky's enforced resignation in disgrace in August 1974.
Cue June 1984, and one Ronald Reagan coming to call. It brings us another excuse to remember that rambunctious song 'Hey! Ronnie Reagan' the sizeable number of Irish dissidents took as their own.
A future Irish President, Michael D Higgins, was among the hundreds who protested at Shannon Airport when Reagan's plane touched down.
The song is bolshie in tone but far from malicious, as you'll see from the refrain: "Hey Ronnie Reagan, I'm black and I'm pagan/I'm gay and I'm left and I'm free/ I'm a non-fundamentalist environmentalist/Please don't bother me."
Writer John Maguire's lyrics also reflected on changes in the intervening 21 years since Kennedy had been feted.
Ireland's banished age of innocence, and no longer total ambivalence about aspects of American politics and foreign policy, is very well caught.
"I remember the show 21 years ago/ When John Kennedy paid us a visit/Now the world's rearranged - not improved, only changed/ But our heart's in the same place - or is it?"
The demonstrators' objections were about US policies in Central America, opposition to nuclear weapons, and Reagan's close relationship with controversial UK prime minister Margaret Thatcher. Mind you, we were later to learn, that last one was not all bad for Ireland.
Still, there was also a great sense of occasion and fun attaching to Reagan, whose great-great grandfather was Irish, and this visit was well received by many. The south Tipperary town of Ballyporeen was en fête to greet the president and he warmly and likeably reciprocated all welcomes.
We are back in far more positive territory when we consider the many visits, in and out of office, by President Bill Clinton and his wife Hillary.
Their first visit in November 1995 was arguably the most politically significant and historically resonant of any US presidential visit.
He was notably the first serving American president to visit Northern Ireland. He had over the years angered the British for his positive interventions in the North's efforts to gain peace.
That first visit was a landmark on that long and arduous journey. Still, there were some of an older generation who were not impressed by his personal life's travails. Unlike JFK, his image, slotted between two popes, will not appear on Irish kitchen walls.
Next up was President George W Bush whose visit in June 2004 is in the same category as that of his fellow party man, Nixon, as it is also largely forgotten. It lasted a net 16 hours but saw some 7,000 security personnel deployed to protect the EU-US summit he attended at Dromoland Castle, in Co Clare.
Apart from the tedium of a stop-start tour of east Clare in a double-deck press bus, dictated by the security funny fellas talking into their sleeves, this writer has only one memory. It was the appearance of Mr Bush in his vest at the window inadvertently aired on television.
But let's not forget that George W was also loyal to the Irish peace process even beyond the ending of his presidential term.
Almost five decades of social and political upheaval on from JFK and 1963, President Barack, er, O'Bama's visit in May 2011, did have a huge feel-good and sense of magic about it.
His "Is féidir linn!" ('Yes we can!') injunction became a rallying call for a nation fretfully trying to shake off recession and gloom. There was also more than a little tongue in cheek.
"My name is Barack Obama, of the Moneygall Obamas, and I've come home to find the apostrophe we lost somewhere along the way," the president quipped.
For all that, Obama - America's first black president - firmly reasserted Ireland's long historic ties to the US.
His emergence into the political limelight also involved alliances with Irish American Democrats. "For the United States, Ireland carries a blood link," he notably said.
So we come to Wednesday and the visit of Donald Trump. Many of us really dislike his politics and his utterances and his general behaviour.
Clearly, some people do like and approve and he still has a big following in the USA. But we must leave all that to one side.
This is the point where we all need to get over ourselves and remember two simple things: this is about the office of president and it is about long-standing and deep familial, cultural, business and other links between two nations which go back two centuries.
Somewhere in the mix, let's note his big investment in west Clare and the local people's acknowledgement of the 300-plus jobs this brings to an area short of employment opportunities. It is doubly insulting to defame local people's realism and good manners.
So, let's keep it simple and focus on two key points:
He is the duly elected US president, and these precious US-Irish links long predate 'The Donald' - and hopefully will persist when he's long gone to that "big White House in the sky".
Otherwise, let's just hope the weather is good and it passes without a glitch.