Godzilla (known in Japan as "Gojira") is the King of the Monsters, one of the most recognizable icons in movie history and perhaps THE most famous movie monster of all time.
History
Created by Japanese production company Toho, and originally appearing in his self-titled black-and-white 1954 film, Godzilla started as a symbol of the folly of nuclear war, a horrific icon of destruction. Basically, he was a dinosaur mutated from atomic radiation, who terrorized Japan. Godzilla movies from 1954 to 1975--sixteen of them in all--are said to be part of the "Showa series," so named because this period of Japanese history is part of the 63-year reign of Emperor Showa (Hirohito.) The "Heisei" series during the 80s and 90s brought seven new movies to the franchise (not including the 1998 American remake,) while the "Millennium" series after 1999 brought six new films before the franchise took a hiatus in 2004.
Godzilla has enjoyed cameo appearances in many other Japanese shows, and he even had his own Hanna Barbera cartoon in the 70s. But overall he's best known for his live action films. The entire franchise has been a battleship of merchandising for decades, with Godzilla spawning multitudes of toy lines and videogames. After his 50th anniversary in 2004, Toho put a halt to the franchise for the third time, and its future remains unannounced.
Godzilla, King of the Monsters American trailer (1956): http://www.youtube.com/watch?v=XnZ6Ktjynh0
Classic Godzilla theme music: http://www.youtube.com/watch?v=o6qAIaqK3_Q
Godzilla cartoon intro: http://www.youtube.com/watch?v=oTItRfN-LO8
Godzilla Nike commercial: http://www.youtube.com/watch?v=1oCF-QFuoYs
Production
With regards to production, the series is most famous for "suitmation," Toho's preferred method of animating giant monsters: basically a guy in a rubber suit, and also for the use of highly detailed landscape and city miniatures. The choreography and realism of the monster suits varies wildly throughout the Godzilla series, and it usually depends on the budget and director at work. Godzilla has been known to fight like a boxer, a wrestler, an animal, etc., and despite his size, he tends to fly spectacularly through the air to stomp or body slam his opponents. Giant monster battles and city-destruction scenes are a flurry of over-the-top pyrotechnics, explosions, and debris, and Toho shunned CGI for most of the effects in the series even when it was readily available.
The human component has always been an important part of the series, and Toho has always provided serviceable (if not outright good) scripts to accompany giant monster mayhem.
Some behind the scenes footage: http://www.youtube.com/watch?v=6JEjphnKacU
Character
Godzilla is a kind of Tyronnosaurus/Stegosaurus looking monster as tall as a skyscraper. He can breath a blue radioactive blast (the spikes on his back start to glow whenever he's about to do so,) and he has monstrous claws, fangs, and a huge tail that he uses to smash buildings and enemies. He's incredibly strong and impervious to almost all man-made weapons. The Japanese defense force always attacks Godzilla with tanks, missiles, and giant masers (a microwave laser,) but they rarely make a dent in him. The only things that usually hurt Godzilla are other giant monsters, and the series is well known for his battles against tons of other classic creatures, like King Ghidorah, Mechagodzilla, and Gigan.
Godzilla is usually shown to be intelligent, even understanding human speech at times, but on rare occasions he's been depicted as a mindless animal. Sometimes, he'll be given a motivation for attacking civilization, such as anger about nuclear testing or environmental destruction, or as a kind of "spirit of vengeance" sent to punish Japan for disrespecting the dead. Other times, Godzilla is a peaceful monster who only wants to be left alone, and has to suffer being mind-controlled by aliens or some other force.
Godzilla's appearance and personality have changed many times over the decades. Although Godzilla started out serious, as the original series progressed, he became less of a villain and more of a hero, (sometimes clumsily) protecting Japan from aliens, monsters, and other threats. The series eventually grew popular with children, resulting in some of the cheesiest and most infamous films in the series, like Godzilla's Revenge and Godzilla versus Megalon (the latter even being spoofed by Mystery Science Theater 3000.) In the 1980s and 90s, during the "Heisei" series of Godzilla movies, the big guy turned heel and became a kind of antihero, destroying Japanese cities while at the same time fighting off monsters. The "Millennium" series turned Godzilla downright evil, and made him a destructive force similar to his 1954 origins (although in the last Godzilla movie, 2004's "Final Wars," he had a bit of hero left in him.)
Two crucial rules always apply to Godzilla, regardless of his disposition: he does not eat people, and he must live on at the end of the movie.
Godzilla's trademark roar: http://www.youtube.com/watch?v=JklxhhSWm0M
A rundown of Godzilla monsters: http://www.youtube.com/watch?v=tCc4OMNgPeA
Critical Analysis
More than just a vessel for giant-sized disaster porn, Godzilla has always represented human (particularly Japanese) cultural fears and prejudices. Whether representing the nuclear terror of the United States during World War II, the danger of environmental devastation and nuclear waste handling, the folly of genetic experimentation gone awry, or the guilt of a country still coming to terms with it's responsibility for war crimes in the past, Godzilla's overtones are hard to ignore.
Unfortunately, through studio interference and the overall dumbing down of the series during the 60s and 70s, the best and most entertaining Godzilla movies are often ignored, with the general publics focus falling unfairly on the most terrible examples of the franchise. While the suitmation effects are still hard to stomach for CGI-soaked Western audiences, Godzilla has seen quite a few moments of action-packed glory, and as with any film franchise lasting as long as it has (James Bond comes to mind,) he's the star of films both delightfully cheesy and sometimes surprisingly poignant. Godzilla retains a cult status all over the world.
On a side note, trust that any English dub of a Godzilla movie--especially from the Heisei era (1984-1999)--is vastly inferior to the original.
My Personal Top 10 Godzilla Movies
1. Godzilla vs. Mothra (1964)
2. Godzilla vs. Mechagodzilla (1974)
3. Gojira (1954)
4. Invasion of the Astro-Monster (1965)
5. Godzilla, Mothra and King Ghidorah: Giant Monsters All-Out Attack (2001)
6. Godzilla vs. Biollante (1989)
7. Ghidorah, the Three-Headed Monster (1964)
8. Godzilla vs. Hedorah (1971)
9. Godzilla: Tokyo S.O.S. (2003)
10. Godzilla vs. Destoroyah (1995)
