Is there an app that will show me total word count across all applications over a period of time? Does anyone know of an application or service that I can enable that will log and record a count of the total number of words that I've typed over the course of a day?

I don't want or need a full keyboard log of all words, and I certainly don't want any of that being stored. I just want to know how many words and characters I've typed over the course of the day, irrespective of application.
Mac Word Counter should help you.

From the above-linked splash page:


  The Word Counter …
  
  gives immediate feedback on your productivity as a writer.
  
  encourages you by showing you your daily output.
  
  gives you clarity about your daily goals.
  
  keeps a complete history of your daily achievements.
  
  assists with finding your perfect writing environment.
  
  counts what counts: words – the ultimate metric for writing.