"The ________ Generation” has long been one of those red-flag phrases, a strong indicator that you may be about to encounter serious bullshit. There are occasions when it makes sense to group together people born during a specified period of 10 to 20 years, but those occasions are fairly rare and make up a vanishingly small part of the usage of the concept.
First, there is the practice of making a sweeping statement about a "generation" when one is actually making a claim about a trend. This isn't just wrong; it is the opposite of right. The very concept of a generation implies a relatively stable state of affairs for a given group of people over an extended period of time. If people born in 1991 are more likely to do something that people born in 1992 and people born in 1992 are more likely to do it than people born in 1993 and so on, discussing the behavior in terms of a generation makes no sense whatsoever.
We see this constantly in articles about "the millennial generation" (and while we are on the subject, when you see "the millennial generation," you can replace "may be about to encounter serious bullshit" with "are almost certainly about to encounter serious bullshit"). Often these "What's wrong with millennial's?" think pieces manage multiple layers of crap, taking a trend that is not actually a trend and then mislabeling it as a trait of a generation that's not a generation.
How often does the very concept of a generation make sense? Think about what we're saying when we use the term. In order for it to be meaningful, people born in a given 10 to 20 year interval have to have more in common with each other than with people in the preceding and following generations, even in cases where the inter-generational age difference is less than the intra-generational age difference.
Consider the conditions where that would be a reasonable assumption. You would generally need society to be at one extreme for an extended period of time, then suddenly swing to another. You can certainly find big events that produce this kind of change. In Europe, for instance, the first world war marked a clear dividing line for the generations.
(It is important to note that the term "clear" is somewhat relative here. There is always going to be a certain fuzziness with cutoff points when talking about generations, even with the most abrupt shifts. Societies don't change overnight and individuals seldom fall into the groups. Nonetheless, there are cases where the idea of a dividing line is at least a useful fiction.)
In terms of living Americans, what periods can we meaningfully associate with distinct generations? I'd argue that there are only two: those who spent a significant portion of their formative years during the Depression and WWII; and those who came of age in the Post-War/Youth Movement/Vietnam era.
Obviously, there are all sorts of caveats that should be made here, but the idea that Americans born in the mid-20s and mid-30s would share some common framework is a justifiable assumption, as is the idea that those born in the mid-40s and mid-50s would as well. Perhaps more importantly, it is also reasonable to talk about the sharp differences between people born in the mid-30s and the mid-40s.
There are a lot of interesting insights you can derive from looking at these two generations, but, as far as I can see, attempts to arbitrarily group Americans born after, say, 1958 (which would have them turning 18 after the fall of Saigon) is largely a waste of time and is often profoundly misleading. The world continues to change rapidly, just not in a way that lends itself toward simple labels and categories.