Kurt Russell has been in some godawful movies. However - he's also been in some great ones. His performance in "Miracle" as Herb Brooks is only one of the many reasons that I've watched that movie about 20 times. Russell's also been in some other classics like "Big Trouble in Little China" and the also BotD worthy Snake Plissken in "Escape From New York"... I never saw "Escape From L.A." though..
For Russell's greatest beard though - we have to go with his performance as R.J. MacReady in "The Thing". I love horror/sci-fi movies and "The Thing" is up near the top of my favorites. A bit of an under-rated movie but it's got a strong cult following. MacReady's beard was exactly what you'd want if you were living Antarctica. Actually.. I think just about everyone in this movie had a beard.