Resting and action membrane potential..?
Answering the question: "Why is a negative membrane potential important?"

I don't think cells have strong feelings about being slightly negative inside its membrane. I'm guessing these are the driving factors:


the cell membrane is nonpolar, so charged particles can only pass via transport proteins. This makes ion gradients an easy way to maintain a source of (literally, in the physics sense) potential energy.
the cell needs to control its environment and send signals to other cells. The particle gradient (sodium, for example), allows it to accomplish these tasks: bring in glucose by co-transporting with sodium, send an action potential by triggering voltage-gated ion channels.
Therefore, the Na/K pump is a way to "charge" the ability of the cell to perform various types of work in the future. 


To risk an analogy, a cell having a membrane potential is like you charging your cell in the morning. You aren't quite sure what exactly you'll be doing with your phone all day, but it will be many different tasks and all will be doable because you've got a controlled energy source.