Pretty sure no one has done 7 straight wins, but I know that Brazil in 1970 had 6 wins out of 6 with no pens or extra time.
Off the top of my head, I know that....
England drew their first match in '66.
West Germany lost to East Germany in the group stage in '74.
Argentina drew with Brazil 0-0 in the second group stage, hence they knew how much they needed to beat Peru by in their last match in order to reach the final.
Italy famously drew all of their group games in '82.
Argentina drew with Italy in the group stage in '86. I think that was the only match where they trailed at any stage.
West Germany...well we know what they did in '90. But they also drew with Colombia in the group stage.
Brazil won the final on pens in '94
France won with a golden goal in round of 16 against Paraguay and on pens in the QF in '98.
Brazil....oh..now then.....maybe they did win 7 out of 7 in '02?
Italy won the final on pens in '06.
Spain lost their opener against SwitzVARland in '10.
Not at all sure about Germany in '14, even though it's the most recent.