I can't really put a time on it. Sometimes I take them down quickly and other times I leave them up for ages and its only when I'm having a clear-out that I put them for recycling.
I'm with lankeela. They are such a waste of money. I don't put mine up. I don't put christmas cards up either, or any decorations. You've only got to take them down again.
Occasionally I will move a pile of junk and find a Christmas card I haven't even opened. What I find really unnecessary is giving a Christmas card to someone you see every day, like work colleagues. Our dog people tend to take a load to a show, written but with no name on the envelope, and give them out if someone gives them one. WTF?
I usually leave them up for about two weeks. Then I put them on the bookshelf in a bundle and sometimes use them as bookmarks, shopping lists, to write a note to someone on..... But some people make them themselves or get something like embroidered ones. These are the problems as they are far to nice to throw away.