I am surprised that some of the most historic universities in continental Europe are ranked above 100 on an average. I specifically have in mind University of Gottingen and University of Vienna. I am assuming that at the peak of their fame, they were rubbing shoulders with the best in the anglo-sphere. What caused the slide in reputation? I have heard that in Germany, Nazism caused the emigration of a lot of talented people. Or is it just that the ranking methodology is biased towards universities in the UK and the US? As someone interested in the history of scientists and scientific institutions, it seems somewhat odd.
First: Rankings are just rankings and are, to a large degree, arbitrary. (Shameless plug: Here is an article (arxiv version here) that shows that for some specific database many players can get to the top rank just by fiddling around with some weights.)
Second: Just as some universities gain reputation, other lose some. That's pretty normal, isn't it?
Last, some trivia: You are probably even more surprised that some universities of some fame in the old days do not even exist anymore. Stupid example: Gauß got his PhD from the University of Helmstedt, a town that has nowaday less inhabitants than some German universities have students… Another example I know of is the University of Rinteln. However, it is hard to judge the standing of these universities at that times. Alas, university rankings did not exist some 300 years ago…
The emigration wave indeed quite dramatically contributed to the decline of at least German research (and, indirectly, due to invasion of neighbouring countries - Bohr, for instance was evacuated - "pseudo-kidnapped" - by the Americans from Denmark). One anecdote was that David Hilbert was asked by the Nazi minister of education, Rust, how mathematics was in Göttingen, now that it had been "cleansed". Hilbert famously replied that there was no mathematics anymore at Göttingen.
Recommended, very well researched reading: Alan Beyerchen, Scientists under Hitler.
One more aspect to be mentioned, of course, is the concomitant rise of the military-industrial complex in the US which was fueled by the exorbitant success of the Manhattan project which showed how foundational science could be converted into direct, tangible uses (again not insignificantly by virtue of the scientists who fled Europe). This, of course, motivated a pouring of inordinate amounts of funding into research in the US, and created a self-perpetuating and -promoting cycle over many decades.
An interesting observation is that these outwardly disparate mechanisms are linked in quite subtle ways.