It would depend, first place, on a working definition of "feudalism". This is far from consensual, with several not very compatible "definitions" being used and abused without much intellectual effort to clarify the issue.
Let's start from these commonsensical definitions, and by criticising them, attempt to reach some conclusions.
One common idea is that "feudalism" is a widely appliable label that can describe almost anything that a) is pre-industrial; b) is no longer egalitarian such as hunter-gatherer societies; and c) doesn't have slavery as a central social feature.
Another common idea is to equate "feudalism" with either "extreme decentralisation without democracy" or outright disorder.
It is easy to see that under the first "definition", a society can only avoid a "feudal" "stage" if it instead bases its pre-industrial inequalities upon slavery. In this sense, yes, any industrial society will have to pass through a "feudal stage" in its way from chipped silex to silicium chips, unless it could someway transition from slavery to capitalism. In that sense, "feudalism" could be seen as a "programmed" event - if you think that humans are bound to superate primitive living conditions.
Conversely, under the second "definition", it is either a non-programmed event, or, if you think that human societies necessarily undergo "cycles" of expansion-stagnation-decadence, a "programmed" event in a circular, rather than linear, "program".
Problem is, these definitions, besides being trite and intellectually insatisfactory, do not describe the same phenomena. One who adheres to the first "definition" would see feudalism in Imperial China, but not (at least not without several qualifications) in China when dominated by warlords. The other would conversely see feudalism in lordwarring China, but not in well ordered Imperial periods of Chinese history.
So what is feudalism?
If we start from history, instead of abstractions, feudalism is, first place, the system that developed in Europe from about the 9th or 10th century on. As such, it features some characteristics that may be absent or present in other societies, such as mediaeval Japan, India, China, Middle East or Africa. Those characteristics may be listed as follows:
Most agricultural production was provided by individual peasant families. Those would have to share their product with landlords, through different mechanisms, namely labour rents (the peasants' access to their land parcels implied the obligation to work in the lord's fields for a given number of days per week) and sharecropping (the peasants' acces to their land parcels implied the payment of a rent in the form of a part of their harvests to the landlord).
These peasants were not slaves (ie, they could not be sold or rented or otherwise treated as property), but they were often serfs, ie, they were bound to land, which they could not leave without express permission of their lords (and, conversely, from which they could not be legally expelled at the lord's whim).
There was a marked social division between rural and urban sectors of society. While there were plenty of rural or itinerant artisans, cities concentrated most of the crafts, and the production there was organised in a remarkably different way. Basically, the common artisan was either a journeyman or an apprentice; both earned wages. Their masters were guild members, and typically were artisans themselves; the guild was an organisation that regulated most of the production and commercial practices, even fixing prices and wages. In theory, apprenticeship was a way for the young artisan to become a master himself; in practice, masters could keep apprentices in such a condition for a very long time, thus maintaing them in dependence.
Both in countryside and city, but more conspicously in the former, there was a characteristic fusion of ownership and political functions. Landlords were typically not only owners of their land, but also it's governors and judges.
The landlords, as a class, were organised in a hierarchic way. Typically, land ownership was a concession from above; a landlord's ownership was inseparable from his relation to a higher landlord (thence a hierarchy of barons, viscounts, counts, dukes, kings, towering above the lower layer of untitled lords), and such relation was a one of political loyalty, implying military duties (mainly meaning the obligation to provide armed men at the overlord's request). That relation between property and poltical-military loyalty constitutes the fief - an extent of land owned conditionally to a fealty tie (and, of course, "fief" is etymologically related to "feudalism").
Estates were in principle indivisible, leading to the huge importance of primogeniture, and to a permanent problem of what to do with further children. This favoured re-centralising tendencies within the system, as higher lords could place those landless noblemen at their service.
The State was paired by the characteristic intitution of Church, which remained basically independent from the hierarchical nobility, provided another outlet for "second sons", a upward social mobility way to integrate exceptional commoners into the ruling classes, and generally worked as a "check and balance" structure to the power of the nobility.
Now, let's see what in this arrangement is merely a quirk of European history, and what is necessary for an unequal society that relies mostly in agriculture.
First, a pesantry organised in individual families (instead of clans), is by no means a given. Most societies transitioned from hunter-gathering into agriculture and husbandry without breaking the clanic systems. And some went hierarchic without such a break either. In places such as the Inca Empire or India, the peasantry remained organised in clans (and some historians would say that this is characteristic of a non-feudal social formation, that they would diversely label as "Asiatic" or "tributary"). So, this feature seems to be not necessary for a hierarchic but pre-industrial society.
But it seems that, barring slavery, the organisation of production in the basis of an exchange of rent for land access cannot be avoided. Wages can only become generalised in agriculture once quite stronger urban markets develop, which is only possible post-industrialisation.
Second, serfdom does not seem to be a necessary feature. And indeed, European feudalism saw a general tendency towards the abolition of serfdom, which generally predated the end of other "feudal" relations, such as fiefs, vassalic hierarchies, rent, primogeniture, etc. On the other hand, serfdom can well be imposed into a clanic peasantry, so it is quite possible that some societies (again the Incas, ancient Egypt) had institutions similar to serfdom without individualised peasant families.
Third, the peculiar urban/rural divide of Mediaeval Europe seems quite original, not being replicated by most non-European mediaeval societies (with the exception of Japan). This is not to say that those other societies did not have a urban sector; rather, non-European cities tended to be mostly political centres instead of manufacturing poles.
Fourth, the fusion of political power and land ownership seems unavoidable, but its precise form in European feudalism is quite peculiar. In other societies, as again among the Incas, and in most of mediaeval Middle East, the State retained land property, and established its "nobles" as governors ("satrapes" as the Persians called them) but without allowing hereditary ownership. The characteristic European personalisation of the political/ownership fusion seems to have been only fully replicated in Mediaeval Japan.
Fifth, again the fief seems to constitute an European (and Japanese) exclusivity.
Sixth, and intimately related to the two previous issues, if land ownership is not to be divided indefinitely, to the point where it would cease to constitute the apanage of an actual ruling class, either primogeniture or State property of land seem unavoidable. Again Japan joins Europe in the characteristic primogeniture rule, but, although I can't claim enough knowledge of these societies, I suspect that Imperial China, as well as Mediaeval India and at least parts of Africa (namely Ethiopia) were under similar rules.
Seventh, if primogeniture is the rule, "second sons" of the nobility constitute a problem, and institutions that attempt to solve it will be necessary. Evidently, the Mediaeval Catholic Church was unique and totally due to the precise history of Europe. But the Japanese samurai (which more closely relates to the European errant knightship, of course) are another, if less complete, attempt to deal with the problem. And one cannot fail to notice the similarites between Tibetan monasteries and those of Europe, although the evolution of each seems to have been completely independent.
So, in conclusion, feudalism seems to be more than a European peculiarity, but less than a necessary stage in the evolution of all societies. But it is probably no coincidence that an early and internally controled transition to capitalism only happened in Europe, and, to some extent, in Japan. Societies that underwent no feudal "stage" or did so incompletely or dubiously seem to have only "progressed" into capitalism as a direct result of European/North American expansion.
Sorry for the verbose answer, but the question is actually quite complex.
For further reference, Perry Anderson's Passages from antiquity to feudalism and Lineages of the Absolutist State, and Barrington Moore's Social origins of dictatorship and democracy provide in depth study of both European and non-European societies and history, of which the above is in some senses an impoverished summary.