You can say "the other generations" if you mean all of the other generations (at least within the scope of the discussion). For example, in the context of Baby Boomers, Gen X, and Millenials, we could say:
Of Baby Boomers, Gen X'ers, and Millenials, Baby Boomers are older than the other generations.
However, if you are only referring to some of the other generations, then you cannot use the definite article "the". For example:
Baby Boomers benefited from post-war prosperity. Other generations were not so fortunate.
In this case, some other generations were not so fortunate, but not necessarily all other generations.