For system admin work, knowing the basics of vi can be really useful when you're suddenly faced with a non-booting system, but you don't need to know much - how to exit being the classic issue. I use vi/vim for really basic editing tasks and switch to something easier for anything more involved (geany being my current choice).
I came in to say this: Learn basic vi (not the extended stuff Vim added) and you'll rarely be out a text editor, even on very stripped down systems. (In my experience, only nano is more common, and that comes with a keystroke cheat sheet at the bottom of the screen while you're using it.) Learn Vim if you actually like vi and want a more featureful experience in the same basic paradigm.
For more modern systems, you can end up in BusyBox and not have access to nano (I think you can specify that vi gets included in BusyBox).