None at all.

A scene in the beginning that takes place on a ship is fairly gruesome. There's decrepit bodies in beds and on chairs and blood all over the walls. The killer, a giant sea louse, is stabbed to death by a man.

As with most Godzilla movies, it's heavily implied that several people are killed in Godzilla's rampage. Lots of destruction.

Some other scenes include: A man on fire, closley followed by a closeup of soldiers being obliterated by Godzilla's atomic breath, a man getting killed by a small explosion (Japanese version only), and a man getting cut in the arm by a drill.

Some smoking.

Godzilla is rather frightening in this entry and may startle some young viewers.

The sea louse in the beginning may creep some out with it's odd appearence and the weird sounds it makes.