That’s a great question. I think it’s a combination of factors as well. It can come down to timing, story, characters, and even more importantly, the actors playing those characters, and the main antagonist creature and how it’s portrayed/conceptualized.
In the case of Alien, first and foremost you have a great movie/story. The characters are great and you really like and care for them. As for the alien itself, nothing like it had ever been seen before. It was and is an incredibly unique design and it was scary as all hell. The combination of those factors make that one special movie.
With Predator, first and foremost, you have Arnold. He was a huge box office draw during that time. His name alone was going to guarantee butts in the seats. Then you had a charismatic cast of testosterone charged characters who each brought something different to this ensemble. They were the Expendables before the Expendables! Now, you put this super team up against a very original and superior alien enemy, throw in some humor and awesome actions sequences, and you have the start of a franchise.
With Godzilla, although he’s been many things to many fans over the years, he too has always been a very original and unique creation. I compare Godzilla to the starship Enterprise from Star Trek (specifically the original). Each was an amalgamation of different things (Godzilla – dinosaur, dragon, sea serpent. Enterprise – flying saucer, rocket, airplane/jet) that came together to form something that was greater than the sum of its parts; again, something not seen before. Godzilla’s never been cookie cutter, from his unique roar, to the shape of his spines, and the fact that he not only breathes fire, but concentrated radiation! The first Godzilla is a cautionary tale, and something obviously that resonates with the Japanese in a vastly different way than the rest of the world. That first movie is so subdued and in stark contrast with most that came after it; for me it’s a very special movie and my favorite.
With these characters, there have been sequels of varying quality and in most cases, diminished returns, but they have had staying power and popularity I think because of their uniqueness. Long live the B monster movie!