How open should I be with my PhD supervisor about the problems in my personal life? My marriage has been going through some problems in the last year which has affected my PhD. My supervisor has been very understanding and was keen for me not to interrupt and granted me a two month extension on my upgrade paper. 

Last week my wife walked out. She came back but this totally put me off my studies. I was supposed to hand in a paper - an optional paper since this was for a journal submission - but I haven't even drafted it and the draft was due tomorrow.

My supervisor knows I have been having marriage problems but she doesn't know any details. Also she doesn't talk about her personal life much and I don't know if she's the kind of person who would be receptive to such details, so I have so far withheld them. Should I tell her my wife walked out? At the moment I have just said there was an incident. She also knows that I have been diagnosed with symptoms of moderate/severe depression, but I thought it best that she knew this since it could affect my work.

Should I carry on being vague or should I test the water and treat her like an intelligent adult and give her more context and details of my issues? Or should I just keep the personal stuff as separate as possible?
I think your vagueness is entirely appropriate and urge you to continue it. As long as your supervisor knows that there are difficulties that cause you to miss deadlines occasionally and as long as you feel she is supportive, there is no reason to say more. It would be a burden for her to know some of these things and yet, she isn't in a position to help you, other than to be understanding and supportive of your studies. 

But you should seek some sort of professional help elsewhere, perhaps at the university if it has a counseling office open to you for this, perhaps elsewhere. 

Also, sharing too much of the problem can start to sound whiney and like you are making excuses for things. 

Keep it light. Keep your relationship to your supervisor professional. Seek personal counseling elsewhere. And good luck.