Spengler has been attacked from every direction, and the attacks are not without force. It is worth taking the criticism seriously before deciding what survives.
The most fundamental criticism is methodological: Spengler's comparisons between cultures depend on his own aesthetic and interpretive intuitions, not on systematic historical evidence. When he says that the Gothic cathedral and Beethoven's symphonies and differential calculus all express the same Faustian prime symbol, he is making an interpretive claim that is genuinely illuminating but is not susceptible to ordinary historical falsification. He cannot be proved wrong in the way a historical claim about a specific battle or political event can be proved wrong. This makes the entire edifice an aesthetic vision of history dressed up as a science of culture. Critics like R.G. Collingwood argued that Spengler's organic analogy is simply false: civilizations are not organisms, they do not have fixed life-cycles determined by biology, and the comparison misleads more than it illuminates.
The second major criticism is of incommensurability. If each High Culture is genuinely incommensurable, if the Apollonian Greek really cannot be understood from a Faustian perspective and vice versa, then Spengler himself, writing from inside Faustian civilization, cannot have genuine insight into the souls of other cultures. His entire comparative morphology would be a projection of Faustian categories onto non-Faustian material. The fact that his comparisons are often illuminating might simply mean that he is a gifted interpreter, not that his morphological theory is correct.
Third, the teleology embedded in Spengler's organic analogy is philosophically suspect. Organisms have life cycles because of biological laws that we understand reasonably well. What would be the equivalent mechanism for civilizations? Spengler never explains what forces drive civilizations through their seasons. The organic metaphor does the explanatory work, but it is a metaphor, not an explanation.
Fourth, the political trajectory of Spengler's ideas is troubling. He was not a Nazi, he explicitly rejected Hitler's regime as vulgar and was marginalized by the Nazi state, but his morphology was taken up by nationalist and authoritarian movements across Europe in the 1920s and 30s, and his own political writings (The Hour of Decision, 1933) advocated for a kind of conservative authoritarianism. The man who wrote that Western civilization was entering its Caesarist phase was at least implicitly welcoming it.
What survives? A great deal, actually, if you disentangle the genuine insights from the methodological overreach. Spengler's critique of Eurocentrism is valuable and ahead of its time: his insistence that each High Culture deserves to be understood on its own terms, not as a more or less successful attempt to be Western, is philosophically important. His analysis of the specific texture of Western modernity, the victory of money over tradition, the substitution of technical expertise for creative genius, the gigantism of cities, the decline of organic community, is often sharply observed, whatever one thinks of the organic framework. And his concept of pseudomorphosis, the way a new culture developing in the shadow of an older, more powerful civilization is forced into alien forms that distort its own expression, is a genuinely useful analytical concept with applications ranging from early Christianity developing under Roman Imperial forms to postcolonial cultures developing under European institutional forms.