As far as morphological type is concerned, there is evidence that, over thousands of years, languages tend to evolve in a sort of circle: synthetic languages tend to become more isolating, isolating languages tend to turn into agglutinating languages, while agglutinating languages gradually evolve towards syntheticity. In an isolating language like Chinese, some of the function-words seem to be gradually losing their status as `words' and becoming `merely' affixes; likewise, in modern English, some of the shorter prepositions in particular often, at least in colloquial speech, show a tendency to lose their full vowels and to become `mere' prefixes (this is often represented in writing by `reducing' `to' to `t'' or `for' to `f'r').
In Paamese, a Pacific-Island language, new verbal prefixes have recently evolved resulting from the blending together of tense and subject-agreement markers: Where older Paamese had a distinct set of tense markers (e.g., `i-' for future tense) and of subject-agreement markers (e.g., `na-' for first-person or `ko-' for second-person), now it has the *single* prefixes `ni-' for `first-person subject, future tense' and `ki-' for `second-person subject, future tense'.
Modern Finnish and Hungarian each have close to 24 nominal cases, yet are clearly descended from a parent language that, as far as we can tell, had much fewer, perhaps only 3.
It is worth noting that, if language change went routinely in a straight line (as opposed to the circular pattern i described above), by now there would almost certainly be no synthetic or agglutinating languages left; bear in mind that human beings have (presumably) been using language for at least a quarter of a million years, and we have good evidence for only the last 2% or so of that period. If it were normally the case that all synthetic languages gradually mutated into isolating languages, but isolating languages didn't mutate into other types, by now there probably wouldn't be much if any evidence at all for the existence, or the possibility, of synthetic or agglutinating languages.
It is also worth noting that, although we can to *some* extent predict what sorts of changes are *likely* to happen, there is no way we can say with any confidence that they *will* happen, or if they do, when. Most of the (Indo-European) languages of Western Europe nowadays are fairly isolating; but the Slavic languages stubbornly retain six of the original seven cases of Proto-Indo-European. Obviously, the speakers of these languages feel there's value in this kind of thing!