Depends on the shot. If it's a family snapshot, then I don't worry about it too much as I'm just documenting a moment (plus, see my story below the pictures). If the shadow is not supposed to be part of the shot, then I definitely don't want it creeping into the shot. Finally, sometimes it's fun to be a part of the shot.
I have another shot, but it's not online so I can't post it. It's my little girl when she was 3 years old, running around at Mount Rushmore. She's running away (playing) since I'm trying to get her to pose in front of the carving for the typical tourist shot. She was having none of it. However, I noticed that as she ran away toward the visitor's center, the monument was reflected nicely in the large windows, along with me taking the shot. It's one of my favorite vacation shots. I took it with a Canon S400 (a great little P&S).