What are some situations when normalizing input data to zero mean, unit variance is not appropriate or not beneficial?
A detailed answer to the question can be found here. 


  [...]are there times when it is not appropriate or not beneficial?


Short answer: Yes and No. Yes in the terms, that it can significantly change your output of e.g. clustering algorithms. No, on the other hand, if these changes are what you want to achieve. Or to put it in the words of the author of the mentioned source:


  Scaling features for clustering algorithms can substantially change the outcome. Imagine four clusters around the origin, each one in a different quadrant, all nicely scaled. Now, imagine the y-axis being stretched to ten times the length of the the x-axis. instead of four little quadrant-clusters, you're going to get the long squashed baguette of data chopped into four pieces along its length! (And, the important part is, you might prefer either of these!)


The take-home-message of this is: always think carefully about what you want to achieve and what kind of data your algorithms prefer - it does matter!