Kissinger's reputation is one that has endured in a positive light, but is not necessarily positive overall. Rather, the controversy simply never grew, given his lack of public involvement in an outspoken way.

Kissinger managed, in the 1948-1998 period, to appear as one of the top 10 most admired men per Gallup polling in their annual lists a total of 11 times. That means for 11 of the 50 years, he was somewhere in the top 10 in admiration. In three of those years, he was the most admired man, outranking the President, because he was more admired than Nixon (1973, 1974, 1975). As noted here, a 1994 poll was one of the last measurements Gallup took of him (and is one of the last ones we can talk about in the past 20 years), which found that, "56% of Americans rated Kissinger on the positive end of a 100-degree thermometer scale, 21% put him in the middle, and just 14% rated him at the negative end".

So, how he remained relatively spotless, although not entirely uncontroversial, is a question to be pondered indeed. First and foremost, Kissinger is considered to have been an extremely effective Secretary of State, and one who took liberties with instructions given by the President, often with good results.

Consider for example the Yom Kippur War in 1973. Near the end of that war, when Israeli troops were encircling and overrunning Egyptian positions, Kissinger was dispatched to "urgently" go to Moscow to negotiate a ceasefire that the Soviets could present to the Egyptians. Kissinger saw, however, that the longer he delayed, the better-positioned the Israelis would be when ceasefire negotiations began. Nixon attempted to stymie this, seeing a ceasefire as more important, and gave Kissinger "full authority" to negotiate, meaning Kissinger could no longer stall by saying he had to consult with the President on terms (Nixon said Kissinger had full authority in a communication with the Soviets, even). Kissinger's craftiness, however, was still quite evident. He arrived in Moscow and insisted, despite their claims that every hour counted, that he would not negotiate until he had a good night's sleep; while he was undoubtedly tired after a 15-hour-flight, this also served to waste half a day, during which time the Israelis continued to advance. This came, of course, at the time of the Saturday Night Massacre (Oct. 20, 1973), so Kissinger was nowhere near that mess. Kissinger began negotiations, and within 4 hours, had gotten the Soviets to agree to every one of his demands (which were different from what Nixon asked for; Kissinger figured Nixon could not impose his will given his weakness at home). He figured that this meant that the Arab states were in a very weak position, and so he decided to try and stall even further, getting Brezhnev to agree that they would allow 9 hours to discuss the agreement with the relevant parties, and 12 hours for the ceasefire to go into effect. Kissinger, of course, then went to Israel. The Soviets had not sent his message informing Israel of the ceasefire for 4 hours, which cut down on their time to continue making advances. In return, Kissinger was once again crafty, telling Israeli leaders that he would "not make a fuss" if military operations continued slightly beyond the ceasefire's start. Suddenly, Egypt's Third Army was trapped and surrounded by the Israelis during this period fully, and Kissinger realized (following a request for joint action by Brezhnev) that Egypt was in even worse position than he'd though before. And again, he was crafty. He began to sign Nixon's name to documents reaffirming the ceasefire, acting as his signer, since Nixon was dealing with Watergate in Washington. And while Kissinger won wars and won favor with Egypt by proposing to reaffirm the ceasefire (that he himself had subtly encouraged to be bent), Nixon fought controversy that Kissinger, around the world, could avoid. It is no surprise, then, that Kissinger's actions in bringing about a peace deal and starting the Egyptian slide towards the United States (in a manner of speaking) were seen by the public as proof that he was a Secretary of State aloof from Watergate and aloof from controversy, who was achieving significant diplomatic gains.

Kissinger managed not only to avoid Watergate's most trying moments while overseas, but he also managed to largely avoid investigation. The special prosecution task force effectively agreed that all of Kissinger's conversations with Nixon were basically national-security matters, and did not subpoena them. Kissinger did allegedly authorize wiretaps that were relevant, and lied to the Senate about it, but Kissinger managed to avoid attention and investigation for this for so long that it never became a prominent issue. Indeed, while Watergate was raging, Kissinger was talking up foreign policy successes, as this 1974 NYTimes article notes, because of his "diplomatic triumph" in getting the "disengagement" agreement between Israel and Syria in 1974 (which officially ended the Yom Kippur War on that front), and he had gotten the Egyptian disengagement agreement earlier that year as well. It certainly didn't hurt that this earned him bipartisan praise at a time when Nixon was falling to pieces.

That's not to say that the wiretapping accusation wasn't revealed. It simply didn't travel far. Kissinger largely ignored it when it was published in May 1973, and while his reputation took a blow, he refused to resign. In fact, Nixon followed up the story by taking full responsibility for the wiretaps himself, which softened the blow to Kissinger. In confirmation hearings, he said he had not recommended wiretapping, but proposed targets for them. He was confirmed, he ended the Yom Kippur War, and he persevered. The stories did not go away, and in June 1974, after the praise for the disengagement with Syria had abated somewhat, stories once again arose suggesting he initiated the wiretaps, rather than just recommending targets. He had a reputation for cleanliness, having avoided controversy until then, and he chose to rely on his foreign policy achievements to get out of the accusations. He held a press conference saying he would resign if the accusations continued, claiming he could not conduct foreign policy if his integrity was at issue. As a result, members of Congress from both parties leapt to his defense, and a resolution in Congress even had broad bipartisan support for his "integrity and veracity". By leveraging his value to the U.S.'s foreign policy, he managed to avoid much further scrutiny.

But let's work backwards a bit. Besides Yom Kippur, how did he emerge from Vietnam with a positive reputation? Wasn't he involved, and didn't he get involved in the secret bombing of Cambodia?

Kissinger here was also quite crafty, and also quite good at managing his reputation. Kissinger managed to avoid attention for Cambodia by, as the principal negotiator, helping secure the Paris Agreements that ended the war. This would remain his legacy, rather than the legacy that included his involvement in that war. He managed, in later memoirs and discussions, to also craft a narrative that while he was conflicted about his part in the war, he also was never fully behind the way it was conducted. That is to some extent an exaggeration of the truth; while he was nowhere near as ardently supportive as some might believe of the war, he was certainly more involved and supportive of bombing Cambodia than he liked to let on. But diplomatic acumen came in handy; during negotiations, he managed to simultaneously balance the desires of the Soviets, China, North and South Vietnam, and the U.S. public, to get the agreement to end the war. His deep involvement in most aspects of the negotiations provided him with the praise and notice of someone who had managed to do something positive, washing away earlier notice of his involvement in the quagmire itself. It didn't hurt, of course, that he was still seen as widely trusted by Congress, and that future Presidents like Gerald Ford and Ronald Reagan all spoke highly of him. Indeed, he continued to be involved in foreign policy long after Nixon, as both an elder statesman and often an appointee to consult on various issues (i.e. part of a team to fight Communism in Latin America under Reagan). Reagan spoke of Kissinger as "'a very distinguished American, virtually a legend in [diplomacy]" to the public, even. Given his ability to remain aloof, and deftly conduct foreign policy while hiding the more unsavory portions of his realist (in the international-relations-sense, this means the belief that power and force are the most important things determining how states interact) foreign policy goals and methods, and his subsequent ability to use those foreign policy achievements to cover over other issues, it is unsurprising that he escaped much scrutiny. Even so, his reputation has not been entirely uncontroversial, and this is visible in more recent historical takes on his legacy.