The annual Leonid meteor shower peaks this year on or around Tuesday night. It's a slow-peaking shower, so even if you go out tonight, or later than Tuesday, you'll probably see a few meteors streaking across the sky.
I've written about them many times in the past; a review is on my Bad Astronomy site, and I wrote a guide to watching the Perseids which is still apropos of the Leonids. NASA's science news page has lots of info, and the International Meteor Organization has technical aspects, too.
Leonids over Uluru image courtesy Vic and Jen Winter at ICSTARS.