What’s The Story With 1–1 Meetings?

Dammit Jim, I’m a software engineer I have no need of social contact!

Something that's always concerned me are the need for 1-1 meetings in software engineering, they just feel out of place somehow. 

Let's talk about the circumstance when you might find yourself in one, what you can do, and why you should pretty much always get out of them if you can.