From the Super Mario Wiki
Frogs (Japanese: カエル, Kaeru) are a species of animals. In the Mario series, real-world frogs exist along with anthropomorphic frogs who are sentient and are capable of speech.
Super Mario Bros. 2
Donkey Kong (Game Boy)
In Donkey Kong for the Game Boy, frogs are allies of Mario. When Mario is standing on them, they jump up high in the air, allowing him to reach higher platforms while carrying the key. Frogs first appear in stage 4-10 in the Jungle. Frogs can also be taken out if objects such as the key are thrown at them.
Super Mario RPG: Legend of the Seven Stars
The Tadpole Pond is inhabited by large, sapient frogs in the duration of Super Mario RPG: Legend of the Seven Stars. Mallow was raised by the frogs (specifically Frogfucius) and believed that he, himself, was a frog as well. The young tadpoles comprise a greater part of the population than the frogs, of which there are only two.
Super Mario World 2: Yoshi's Island
Smaller frogs later appeared in Super Mario World 2: Yoshi's Island where they could be seen jumping around in some World 3 levels, they didn't have any effect on the gameplay and were mostly part of the background, also red and green frogs could be seen in the foreground of swamp stages (they are also unaffected by gameplay and were simply placed in the game for decoration). The game also features a sub-species of enemy frogs known as Frog Pirates and there was also a Frog Pirate boss called Prince Froggy.
Diddy Kong Racing
In Diddy Kong Racing and its remake, several frogs live in the pond in the hub. One of these frogs, who has a tell-tale red crest upon its head, is actually Drumstick, who has been put into frog form by Wizpig. He can be freed if the player runs over him in a car.
Mario Party 6
Frogs make minor appearances in WarioWare series. In WarioWare: Mega Microgame$ microgame What's the Toadal?, frogs must be counted. Strange-looking frogs appear in the Nature folder microgames Hoppin' Mad and The Frog Flap. In WarioWare: Twisted, orange frogs appear in Launchpad.
Luigi's Mansion: Dark Moon
Frogs appear again in Luigi's Mansion: Dark Moon. In this game, they are red, croak when discovered, and act as ambiance creatures. They don't directly try to injure Luigi. They also appear in the final King Boo battle, as well as a special giant version of the frog, which may appear instead of a spiked ball when King Boo slams the ground. Like other ambiance creatures in the game, there is also a Gold Frog variant, which will reward Luigi with multiple Gold Bars if he uses the Strobulb on them.