This is not normal or safe. You need to tighten your headset.
You should loosen the clamp bolts on the stem and tighten the bolt on top of the steerer tube. This will compress the space between the stem and the headset, removing the slack. It should be tight so there is no play, but not too tight that it creates friction when turning the bars.
Here is a link explaining the process more:
http://www.artscyclery.com/learningcenter/tightenyourheadset.html