Several of these analogies have been lucidly argued elsewhere, and I've provided relevant links. Whether history rhymes or repeats, these patterns may prove instructive to anticipating the near future.
1. The end of the Belle Epoque and the Eve of the First World War. We don't need more essays despairing the rise of nationalism in turning politics away from globalism, heralding the end of the Davos order, but the rational detente of late 1800s Europe fell apart quickly in the face of nationalism and entangling alliances. Trump's election by nationalists and his entanglements with Russia expose this similarity. Today, Russia increasingly tests whether people in Cleveland want to risk a nuclear war over Lithuania. Little appreciated today is the shock World War I represented for globalism (or at least European internationalism), resulting in a decrease in international trade that didn't return to pre-WWI levels until the 1970s. For me, this analogy is the most poignant of all that I list here, since there are clear cyclical waves trade and political relationships, some of them quite macro. The most obvious is the onset of the middle ages in Europe after the fall of Rome, but even this was a repeat (and a pale one) of the dark ages of antiquity, the late bronze age collapse in the Mediterranean. A decrease in international relationships is of obvious advantage to regional powers with chronically anemic economies but large militaries, like Russia.
2. The Washingtonian Dynasty Losing the Mandate of Heaven. It's a truism that Chinese dynasties last on the order of two centuries. This pattern holds for other large states. Taking the Roman Empire as a succession of two states punctuated by the Crisis of the Third Century, we have two dynasties of not quite two centuries. The U.S.'s founding moral authority and legitimacy stem from our belief in the specialness of our constitution. Though I count myself a patriot I must admit that if I heard an Australian or Mexican or Indian talking about her constitution with the same unquestioning reverence that we hold toward our own, it would seem rather strange. Red and blue state Americans have not begun to question the constitution in earnest as much as have irreconcilable ideas of what it means. If the American Civil War was nearly a North-South constitutional echo of the East-West scriptural schism of Europe, this may be the Reformation. What has suddenly exacerbated this difference? One possibility is a status monoculture brought about by social media. There are few things worse by being looked down upon by morally illegitimate people, pretending to be in the right based on the principles that only your own side understands.
3. The internet as the printing press and the American cultural divide as mid-millennium Europe's Protestant-Catholic divide. The internet and in in particular social networks have suddenly and inescapably forced on Americans the realization that there are people elsewhere in our own country with fundamentally different values than our own, and different ideas about the origins of our government's moral legitimacy. This is problematic, because humans really have only three ways of dealing with the "other": remain ignorant of them (which we no longer can), convert them, or decide that they are subhumans/gentiles/outlanders who are not worth converting (or to whom conversion can or should not apply). In mid-millennium central Europe, the printing press not only spread ideas but spread awareness of the people in the city next door who despise your moral authority and who might even try to force you to follow theirs. Even empires cannot comfortably or sustainably solve the disappearance of moral-authority silo walls; the Ottoman Empire had the unique solution of millets, but even this was uneasy and eventually collapsed. For a much more thorough treatment of aspects of the Thirty Years War analogy see Venkatesh Rao's essay.
4. The end of the Whig party and Trump as Zachary Taylor. Of course, part of this story must be the dramatic realignment of political coalitions occurring on both sides of the Atlantic,a shift similar to but more profound than the cultural-coalitional mismatch Nixon exploited in his Southern strategy. That realignment is the shift of cultural conservative blue collar whites into the GOP and the more surprising transformation of wealthy coastal professionals into the Democrats. It's absurd to assume that a country of 320 million can be adequately represented by two political parties, and surely both major parties have their contradictions, but the GOP's tripolar values of God-country-market is far more explosive. In practice, those three values reduce to two values - respect for authority, and individual freedom - because God and country largely covary. Respect for authority versus protection of individual freedom further correlate closely with intelligence and education, and the basic cognitive divide that modern economies and elections expose are vexing for traditional coalitions of conservatives and liberals alike. (Odd, that educated liberals fight for entitlement programs that in many places are going to uneducated people to collect while they sit at home watching FOX.)
The analogy here is between the GOP and the Whigs, an American national party that died in the 1850s with an outsider President, driven by internal conflict over a question that exposed their divisions. When slavery was was forced to the center of national attention by the admission of southerly states after the Mexican War, the Whig coalition (of Northern industry-men and Southern plantation owners) disintegrated - having until that time been held together by their hatred of over-reaching Federal executive Andrew Jackson. As we are learning, a party that knows its values only in opposition to a hated enemy can rarely sustain itself. Mexican War general Zachary Taylor was a complete outsider to politics who was elected as the last Whig President. It might be mentioned here that if you count up the governors and members of Congress who came to their position with no history in politics, you'll notice that Republicans dramatically outnumber Democrats. The President is only the most dramatic such example. For an expansion of this analogy see Gil Troy's essay.
5. Trump as Carter. I won't belabor this one except that a) you can’t do much better than this essay by Julia Azari and b) pushing the analog probably too far, that would make Obama the Democratic Nixon, rather than the Reagan. Aside from the paranoid streak that was Nixon's undoing, this would not otherwise be an insult: both were tireless public servants and serious policy wonks, with pragmatic centrist styles. (Nixon a centrist you say? He established the EPA and laws protecting whales, removed the U.S. from the gold standard, and proposed national health insurance, which may today be as unbelievable as Obama defending the TPP may appear in a few decades