The streak will be ended by one person and one person only: The Undertaker. When he decides that enough is enough and that he doesn't want to defend it any more, that's when it'll end.
The Undertaker will face John Cena at next year's Wrestlemania in what will be his final match. If Taker wins, then he rides off into the sunset. If Cena wins, then you'll have the heel turn that everybody's been waiting for, well, ever lol.
But IMO, Taker retires undefeated.
I get they logic behind why some people say Kane, but realistically, what would beating the streak do for Kane? He's a guy who's himself in the twilight of his career. The long term rub that would come with beating the streak would be wasted on a guy who's coming to the end of his career like Kane.