My favorites (in chronological order):
Gojira (obviously)
Mothra vs. Godzilla
Ghidorah, the Three-Headed Monster
Destroy All Monsters (I know the film itself doesn't hold up as well, but it's still a good time and knowing what all went into that final battle just makes it amazing as hell to behold)
Godzilla vs. Hedorah (I know, I'm demented)
Terror of Mechagodzilla
Godzilla vs. Biollante
Godzilla vs. King Ghidorah
Godzilla vs. Mechagodzilla II
Godzilla vs. Destoroyah
Godzilla vs. Megaguiras
Godzilla, Mothra, King Ghidorah: Giant Monsters All Out Attack! (Probably my favorite Godzilla film after the original and my fifth favorite kaiju film after the original and the Heisei Gamera trilogy, which is amazing, pick up the Blu Ray of it ASAP! Seriously, it's only about 8 bucks for the entire trilogy! Do it!)
Godzilla Against Mechagodzilla/Godzilla: Tokyo S.O.S. (Kiryu is my second favorite kaiju behind Spacegodzilla and Akane is possibly my favorite human character)
Worst:
Godzilla Raids Again (boring as hell)
Godzilla vs. the Sea Monster (every single scene in this movie sets off my bullshit receptors)
All Monsters Attack (I know it's made for kids, but still, even as a kid I hated it. Hell, my three year old barely had any interest in it)
Godzilla vs. Spacegodzilla (which pains me to no end, as I said above, Spacegodzilla is my favorite kaiju. This is a fully phoned in movie across the board. Transforming Mechagodzilla into Mogeura? Ugh. Add to that the painful asteroid field battle and you've only scratched the surface of this horrid movie.)