The best annual meteor shower is the Geminids, which are expected to peak this year on December 13th at 18h. Some activity will persist until about Dec 15/16. Unfortunately this year's display will be spoiled by a Full Moon at maximum, but you should still see some of the brighter meteors.
The ZHR (Zenithal Hourly Rate: the standard measure of meteor activity) is predicted to be around 100, but you will probably only see about 1/4 of that rate because of the Moonlight. Grab any few hours when the Moon is out of the sky on the days on either side of maximum to get the best view, or if the Moon is up, position yourself so that it is hidden behind a tree or building if possible. The radiant is just North of Castor in Gemini.
Check this website to see how many meteors are this year - and submit your own observations! This is a live count of meteor showers based on visual data entered through the IMO electronic report form. It is made by Geert Baresten, now a PhD student at Armagh Observatory.