I just remembered this topic, and I thought I should explain why I think the Godzilla movies I chose to be my favorites are so great. Before I go on, I must explain that when I do a movie synopsis, I don't like to put much focus on the plot, because I want the viewer to watch these movies and figure out the plot for themselves. I may insert mild plot spoilers to point out some reasons why I like these movies, but that's as far as I will go. Enjoy.
Gojira: The first of the series and quite obviously the best. This movie represents the events of Hiroshima and Nagasaki, and the fear, pain, and suffering that the Japanese felt during these events. In this film, Godzilla (called Gojira in Japan) is the physical embodiment of nuclear warfare, and lays a path of destruction all over Tokyo. What made this movie for me (other then Godzilla destroying Tokyo) was when Dr. Daisuke Serizawa hesitated to use a weapon of mass destruction he created to stop Godzilla, because he feared that if everyone saw it, every nation on the planet would want one and force him to make more. I highly recommend this movie to ANYONE, even if your not a fan of monster movies.
GMK: Giant Monsters All-Out Attack: Now this is a good Godzilla movie. It had great acting, detailed suits and Mothra puppet, FANTASTIC special effects, and vicious monster fights. The only thing that I didn't like about this movie was that King Ghidorah was portrayed as a hero. In my opinion, Ghidorah should ALWAYS be a villain. However, I do realize that two daikaijus, Anguirus and Varan, were replaced with Mothra and King Ghidorah so that more people would want to watch it (later two daikaijus are MUCH more popular than the former two). If you want to see epic monster battles, this is one to see.
Godzilla vs. Mechagodzilla II: This movie wowed me the first time I saw it. Godzilla, Mechgodzilla, and Rodan were an excellent cast of daikaijus, but what surprised me in this film was how well BabyGodzilla was portrayed. Usually, Godzilla's son (he's adopted, NOT reproduced by Godzilla) isn't the type of character that fans go head-over-heels for, but to me, he's the most adorable and sympathetic character since E.T.. Although the plot seems to focus on the baby, this movie isn't without a few daikaiju fight scenes. In fact, these battles are some of the best in the entire series. If your a Godzilla fan and haven't given the chance to see this gem, do so and enjoy that you did.
Godzilla and Mothra: The Battle for Earth: This movie holds a special place in my heart, because it is the reason why I became a Godzilla fan. It was the second Godzilla movie that I have ever seen (the first was King Kong vs. Godzilla), and it was like love at first sight. The special effects were great, Godzilla was great, Mothra and Battra were great, the fights were great, the plot was great (IMO), etc.. When I'm in the mood to watch a Godzilla movie, I usually end up watching this one. If this movie got me into the Godzilla franchise, it can get anyone into Godzilla as well.