The funny flying turtle is Gamera. He had his own series of movies which were far worse than the Godzilla films (Love 'em all anyway).
I'm afraid good old Godzilla is neither the misunderstood animal making it's way through the city or hero any more. For some reason they remade him and he's an evil lookin critter now. The series all continue over seas. We just don't get them here. Mothra has gone through a few new movies (and new abilities - fish form and space/time travel form as well as some electric beam type weaponry). The Mothra series seems to be aimed more at the Japanese children.
I've got alot of the old films on CD.
I still love War of the Worlds (both versions)- watch it every time it comes on.
The first Godzilla (Duh!)
When Worlds Collide
Oh so many to choose from!
I really miss the Saturday Creature Feature or Sci Fi Matinee on the old UHF channels. It was great getting a scare in the afternoons and play at space rangers, vampire hunters, or whatever after the movie.