The Leonid meteor shower has been responsible for some of the most spectacular celestial displays in history. Most recently, there were several extremely intense Leonids from 1998 to 2002, with some observers reporting more than 1,000 meteors per hour.
Meteor storms like these happen only around the time that the parent comet, 55P/Tempel-Tuttle, makes it closest approach to the Sun. Tempel-Tuttle is now far from Earth and the Sun, so the 2007 Leonids are expected to be modest, with no more then 10 meteors visible per hour. However, the Leonids have yielded surprises before, so they're always worth watching.
The shower peaks on the night of Saturday–Sunday, November 17–18. Leonids start to be visible after the shower's radiant rises above the horizon, around midnight at mid-northern latitudes. Conveniently, the Moon sets around the same time. You're likely to see increasing numbers of meteors as the radiant gets higher toward dawn.
As long as you're outside in the early morning, don't forget to look at the sky's other attractions. In addition to all the brilliant winter stars, several bright planets are on display. Mars blazes at magnitude -1 almost directly overhead. Saturn climbs into the sky not far behind the Leonids' radiant. And Venus clears the eastern horizon around 3 a.m.
And of course, take a good look at amazing Comet Holmes, which is well above the horizon all night long.