On the night of Tuesday/Wednesday August 11/12, the annual Perseid meteor shower will peak. If you find a dark spot and go out after midnight, you should see up to 60 or so meteors zinging across the sky per hour. This year is not as great as previous years, since the Moon will be up almost all night and washing out the sky somewhat, but if you make the effort I'm sure you'll see quite a few shooting stars.
For the 2007 Perseids I wrote up a post called 12 Things You Need To Watch the Perseid Meteors, and nothing really important has changed since then, so reading that will give you a good guide on what you need to do if you want to watch the show. One thing that has changed since then, though, is the advent of Twitter! It has a lot of uses, including those astronomical and meteorical: the Newbury Astronomy Society has started Twitter Meteorwatch, where you can follow the Perseids online, get links to live webcams, and ask questions about the shower as well. Just use the hashtag #Meteorwatch when tweeting. If you're interested in observing the shower, I urge you to find groups going out; it's more fun with lots of people, and it's easier to stay awake. Sky and Telescope's website has a searchable list of clubs and organizations so you can find out who's near you. Added bonus: Jupiter is up all night, so if you're with a group of folks with telescopes you'll get to see one of the best sights in the sky. Bring binoculars if you have them too; they're easy to share. The Perseids are a great way to get kids into astronomy, and a wonderful way to spend an evening. Have fun!
Perseid image courtesyaresauburn™'s Flickr stream, CC licensed.