Star Wars: The Empire Strikes Back
Mad Max: The Road Warrior
Indiana Jones: Raiders of the Lost Ark
Lord of the Rings: The Fellowship of the Ring
Die Hard: Die Hard I
The Thin Man: The Thin Man (1934)
I assume you're thinking of franchises consisting of more than two movies?
The Matrix
Back To The Future
Jurassic Park
Pirates of the Caribbean
Jaws
Home Alone
The Mummy
The NeverEnding Story
Halloween
I Know What You Did Last Summer
Friday the 13th (okay, the first one isn't exactly a masterpiece either)
I'm not too fond of the other The Godfather movies either.
Great choices. I would have once agreed with you on "The Godfather" but over time I've come to appreciate "II" as well -- "III" is still good for nothing but unintentional hilarity.
"Planet of the Apes"