The Draconid Meteor shower is due Saturday October 8, 2011, right in time for World Space Week. In addition, Saturday is also International Observe the Moon Night. Sounds like perfect reasons to go take a look outside at night.
This video from NASA (has an ad) will explain more.
If you miss the Draconid shower or it doesn't turn out to be much of a show, try the Orionid meteor shower which is supposed to peak in the early morning of October 20 and 21, 2011. Unfortunately, the brightness of the moon may interfere.
1. Try to find a place that is dark for best viewing. Porch and street lights can fade out the meteors.
2. Remind your children there may be several minutes between sightings. In the wee hours of the morning it can be hard to be patient.
3. Blankets and lawn chairs that allow for viewing in a prone position help prevent neck strain and keep chilly viewers warm.
More information at EarthSky
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Photograph from NASA by Vincent Jacques