I don't see why anybody would be against this, especially since these games didn't feature Bowser as the main villain (or at least, the "final boss"):
-
Super Mario Bros 2 ("Super Mario USA" or "Yume Kojo: Doki Doki Panic" in Japan)
-
Super Mario Land
-
Super Mario Land 2: Six Golden Coins
-
Mario Party 3 (Story Mode)
-
Mario & Luigi: Superstar Saga
-
Paper Mario: The Thousand-Year Door
-
Super Paper Mario
-
Mario & Luigi: Bowser's Inside Story
-
Paper Mario: Color Splash
(You actually fight the "Black Paint" instead of Bowser, who was oblivious of what was going on the entire time he was being taken over)
-
Mario Tennis Aces
-
Paper Mario: The Origami King
-
Mario Golf: Super Rush
-
Mario & Luigi: Brothership
Of course, this may not be the entire list, but just the ones as far as I know (and what I've played).