How many times must we live through these throat-paralyzing sequences of days of gun play, grief and muffled drums?

The question, posed by LIFE magazine in its June 14, 1968, issue, is freighted with all of the wrenching emotions unleashed by the events that so unsettled the country and the world in the first half of that schizoid year, 1968. The  assassination of Dr. King; the Tet Offensive, the My Lai massacre and all the other horrors attendant on the war in Vietnam; and, on June 5, the murder of Robert Kennedy by a Jerusalem-born Jordanian, Sirhan Sirhan, in the kitchen of the Ambassador Hotel in Los Angeles.

Here, on the anniversary of the assassination — a murder made, if possible, all the more heinous by the fact that RFK appeared to be finding his voice as the leader of a vast, disaffected cross-section of the American populace when he was gunned down — LIFE.com presents a series of pictures by the great LIFE photographer Bill Eppridge, many of which never ran in the magazine.

The very first image in the gallery, of course, has become not only the most recognized picture from that chaotic, hellish event, but one of the most chilling, signature images of the 1960s. As a historical document, it’s indispensable. As a photograph, it’s astonishing: made in an instant, Eppridge’s picture possesses the immediacy of great photojournalism, while somehow conveying the totemic sense — especially in its interplay of (barely perceptible) light and (profound) dark — one sometimes gleans from portraits by the Old Masters: Rembrandt might have felt a kinship with the lighting and composition of the scene.

The nation in less than six years [LIFE continued] has watched the violent deaths of two Kennedys and a King. If Robert Kennedy, a complex man, ambitious and fatalistic, did not inspire so universal as admiration as his brother, he had shown himself capable of growing and deepening. He died too young; the Kennedy family has paid dearly or its ardor for public service.

Almost instinctive in the recoil at his murder was the sense that it was a part of a climate of violence. Arthur Schlesinger [JFK's "court historian"] may have been speaking more in the moment than as a historian when he said last week “we are today the most frightening people on this planet.” Even if he is a Pasadena resident, a Jordanian Arab [RFK's assassin, Sirhan] who kills out of a hatred for his ancient enemy, the Jews, may be a better example of classic Middle eastern methods than of the callous kook our mixed-media society is accused of turning on and turning loose.

President Johnson was right when he said, “Two hundred million Americans did not strike down Robert Kennedy…” But it is surely a good thing to ask ourselves whether the compulsion to violence was born entirely within a killer or whether we and our society are somehow accomplices…. The Vietnam was has been our most vivid daily exposure to violence — and the nation’s eagerness to stop it comes less from any political reappraisal of the ends than a moral revulsion at the means: we don’t love violence all that much.

In the decades since LIFE’s readers encountered those sentiments, millions of words have been written about the Kennedys and, specifically, about the abiding intensity with which President Lyndon Johnson and Robert Kennedy despised one another. (The two men had been enemies — not too strong a word — ever since LBJ accepted JFK’s invitation to be his running mate, a decision Bobby Kennedy vocally fought until, and beyond, the 1960 Democratic convention.) But in early June 1968, it was still possible for most Americans to believe that the president might, in fact, genuinely mourn the loss of the dynamic — if chimerical and often arrogant — Robert Kennedy.

The remarkable photographs that Bill Eppridge made before, during and after RFK’s assassination don’t require that we forget all we’ve learned about the dank underside of American politics in order to appreciate the fear, rage and profound anguish sparked by Robert Kennedy’s death. On the contrary, the pictures in this gallery suggest that despite how ambitious, manipulative and even cruel he could sometimes be, Bobby Kennedy obviously inspired, in countless people, the better angels of their nature.

(One person whose better angels were clearly not stirred was Sirhan Sirhan, who murdered Bobby Kennedy because Kennedy supported Israel, or maybe because he (Sirhan) was drunk and enraged on the one-year anniversary of the beginning of the Six-Day War in the Middle East, or perhaps because he was brainwashed … take your pick. Sirhan’s stated reasons for pumping three bullets into RFK have varied wildly through the years. What is not in dispute is that he did the crime.)

Would RFK have won the Democratic nomination if Sirhan had not murdered him in the kitchen of the Ambassador Hotel? Would he have gone on to beat Richard Nixon in the general election if he had won the nomination? Playing “What if …” is always an intriguing, if ultimately pointless, exercise. The real measure of the man, however, has to be taken not by what he might have done, but by what he actually said and what he did during his lifetime. “A complex man, ambitious and fatalistic,” LIFE called him, a man who had “shown himself capable of growing and deepening.” We’ll never know how much he might have grown, how much further he might have deepened, had Sirhan’s bullets not silenced him. In the end, that’s where the real tragedy lies — in the ruined promise of a murdered human being’s potential.

Robert Kennedy was 42 when he was killed. He and his wife, Ethel, had 11 children; the last, Rory, was born six months after the assassination. Sirhan Sirhan is now 68 years old, and serving a life sentence at Pleasant Valley State Prison in California. He has a parole hearing every five years.