When I am not 'training', rest days are just that. But, when I am getting prepared for an upcoming event, I will step it up a notch and usually at least do some weights on off days, if not a short run or tennis or biking or whathaveyou.
That's funny, I am just the opposite. When I am training, Monday is always a rest day and that means nothing. I do stretch a little every day when I'm being consistent, but nothing else. I feel like I need one day off to not burn out because I get so intense when I am really training. When I am not formally training and just running for maintenance, I just call them non-running days and do whatever I feel like, often yoga, walk, rollerblade, and sometimes nothing, but that's rare. Those are more fun workout days.