Spengler's influence has been surprisingly great. He is often credited with spawning both the popular Cyclical Views (of society/politics) and Culture/Civilization Views of late:
His view of (all human) societies can be (incompletely) summarized in something like the following:
I sometimes think Spengler makes Hobbes look cheery!
I actually agree with the great bulk of his work but think it lacks operationalized specificity (and therefore resists scientific constraints like testability). Besides those well-known objections (raised by Popper and others, long before), I'd like to throw a few more into the ring:
Spengler is himself an agent of history and the metaphor is itself a primary symbol or image of Western Thought (Wittgenstein's Picture Theory of language for example). Metaphors as a concept to be analyzed, considered, thought about, and traded like intellectual commodities failed to exist, formulate, or reify in previous societies. Is Spengler's critique of history only a Western critique (by the logic of his own theory) thereby? (My disdain for the use of naive pictures to guide philosophy is well-known - such metaphors are implicitly invoked, rarely defended, do most of the real-work of the theories that rely on them, and are dogmatically held in spite of any reasons to do so.)
Money is itself a construct and symbol of Civilization. He himself notes that money's nature and relationship to society changes (during the transition from Culture to Civilization). Indeed, the increasing ephemeralization (and abstraction) of money seems essential to its gaining all-encircling power. With advances in economic thinking, monetary policy, and finance money itself can be deliberately crafted (as well as its interrelationships with and to people)! Perhaps, the inevitable and dismal sequence of events Spengler foresees is not quite so inevitable after all!
Spengler invokes a discontinuous metaphor (again a picture) that others like Kuhn have also employed (e.g. - the incommensurate in The Structure of Scientific Revolutions). This, by itself, appears to be dubious (given the slow, subtle, but quite constant accretion of global knowledge). Prior to the late 20th century such knowledge was perhaps invisible (to those cloistered armchair philosophers who also lacked much professional experience outside academia) - now, it's undeniable. Civilizations falter and collapse in their totality - math, science, and general knowledge live on affecting all subsequent societies. On that basis we might therefore challenge the circularity/cyclical metaphor he employs as well.