The most visible meteor shower in most years are the Perseids, which peak on August 12 of each year at over 1 meteor a minute. A useful tool to calculate how many meteors per hour are visible from your observing location is found here: http://leonid.arc.nasa.gov/estimator.html.
The most spectacular meteor shower is probably the Leonids, the King of Meteor Showers which peaks on a day near 17 November. Approximately every 33 years the Leonid shower produces a “meteor storm”, peaking at rates of thousands of meteors per hour. These Leonid storms gave birth to the term “meteor shower”, when it was first realised during the November 1833 storm that the meteors radiated from near the star Gamma Leonis. The last Leonid storms were in 1999, 2001 (two), and 2002 (two). Before that, there were storms in 1767, 1799, 1833, 1866, 1867, and 1966. When the Leonid shower is not storming it is less active than the Perseids.
Other notable strog meteor showers are Quadrantids and Geminids.
The Geminids are a meteor shower caused by an object named 3200 Phaethon, which is thought to be an extinct comet. The meteors from this shower can be seen in mid-December and usually peak around 12-14 of the month. The Geminid shower is thought to be intensifying every year and recent showers have seen 120-160 meteors per hour under optimal conditions. The Geminids were first observed only 150 years ago, much more recently than other showers such as the Perseids and Leonids.
The meteors in this shower appear to come from a radiant in the constellation Gemini (hence the shower’s name). However, they can appear almost anywhere in the night sky, and often appear yellowish in hue. The meteors travel at medium speed in relation to other showers, at about 22 miles per second, making them fairly easy to spot. The Geminids are now considered by many to be the most consistent and active annual shower.
The radiant f the Quadrantids is an area inside the constellation Boötes. The name comes from Quadrans Muralis, an obsolete constellation that is now part of Boötes. It lies between the end of the handle of the Big Dipper and the quadrilateral of stars marking the head of the constellation Draco. Adolphe Quetelet of Brussels Observatory discovered the shower in the 1830s, and shortly afterward it was noted by several other astronomers in Europe and America.
Peak intensity is exceedingly sharp: meteor rates exceed one-half of their highest value for only about 8 hours (compared to two days for the August Perseids). This means that the stream of particles that produces this shower is narrow – and apparently derived within the last 500-years from some orbiting body. The parent body of the Quadrantids was recently tentatively identified (in a paper by Peter Jenniskens) as the minor planet 2003 EH1, which in turn may be the same object as the comet C/1490 Y1 [2] which was observed by Chinese, Japanese and Korean astronomers 500 years ago. The best date to view the Quadrantids is January 3, although they can normally be viewed on any day from the 1st to the 5th of the month. The radiant rises after local midnight.