The annual Leonid Meteor Shower runs its course between the 14th and the 21st. Like other meteor showers the Leonids have a peak time when the meteor stream entering the upper atmosphere is most intense. The peak times based upon previous years is calculated to be between the 17th and the 18th. The number of meteors to be seen on the average each hour is referred to as the ZHR, or Zenith Hourly Rate. For the Leonids the ZHR is typically around 10 or so.
The Leonids have an interesting history of producing a meteor shower with a ZHR in the tens of thousands. This incredible event, a meteor storm, occurs at roughly 33 year intervals with the most recent 33-year period ending during 1999. However the predicted storm of 1999 was not as intense as expected nor were the Leonids of 2000 that impressive. Sometimes, as what happened one century ago in 1899, the storm occurred a few years later than predicted.
This year the Leonids should have a good display as the stars of Leo and the radiant for the meteor shower rise around midnight local time and the Moon sets a couple of hours later. This puts Leo well up above the horizon in a relatively dark sky before sunrise and with no moonlight to brighten the sky and interfere with viewing.

Click here for a graphic showing the location of the Leonid Meteor Shower at 6 a.m. CST on the 17th of November.
Also in this image is Comet 103P/Hartley.