What a great thread.
I do just what I do here.
That is, I assist researchers (mainly academic) understand and apply statistics to their data. I do both pure consulting, i.e. advising, as well as some projects, and I'm planning on adding some workshops in the near future. I used to do this in a university statistical consulting office, but am now on my own.
I was ABD in social psych when I realized the only part I liked about *doing* research was analyzing the data, so I left with my masters and got a masters in applied statistics with the one year I had left of a fellowship. Consulting in academia has turned out to be a perfect fit for me.
Karen