BACK AWAY = move in backward direction; retreat

They backed away from the boy wielding a knife not wanting to get stabbed.

BACK DOWN = stop defending yourself or your opinion

Christina never backs down. She loves to argue and usually wins.

BACK INTO = enter a parking space or hit something in reverse gear

He backed into the fire hydrant because he couldn’t see it in the rear view mirror.

BACK OFF = retreat; make space

You better back off a little if you want me to start serving this crowd again.

BACK OUT = A. go in reverse direction B. to not keep a promise or to not show up

A. She backed out of the garage carefully to avoid scratching the paint.
B. The band backed out of the concert but we got a refund for the tickets.

BACK UP = A. support B. copy C. move backwards, reverse

A. Good thing John was there to back up your story.
B. Back up your files onto a CD so you don’t lose them.
C. Could you back up a little so I can see the screen, please?  

Ojo :

C. sounds strange to me...I would say "move back a little", but back up?

"Back up" is  often used when talking about vehicles,one can "back out" of a parking place, for example. This means not only to "back up" but to also be exiting.And one can "back out" of a situation. ( Courtesy of Richard Chanel , from Brooklyn )