From Sonic Retro
Froggy, known as Kaeru-kun in Japanese, is the amphibian pet of Big the Cat. He debuted in Sonic Adventure, where the goal of Big's levels was to fish Froggy out of whatever dubious water feature he'd hopped into this time. The green creature has accompanied Big in all of his non-cameo videogame roles. Big acts as though that he and Froggy (and other frogs) are able to freely communicate with each other, but this may just be his imagination.
Aside from serving as his slow-witted keeper's level-by-level goal, Froggy became critical to the plot of Sonic Adventure by swallowing a Chaos Emerald along with a portion of Chaos' tail. Consequently, Dr. Eggman dispatched the E-100 Series to capture the amphibian, making Froggy an objective in one of E-102 Gamma's missions. Chaos' absorption of Froggy and re-acquisition of its tail caused the beast to take its Chaos 6 form.
Froggy was kidnapped in Sonic Heroes by Neo Metal Sonic, apparently so the robot could extract any lingering information about Chaos' shape-shifting abilities that might have remained within the frog after Sonic Adventure (Metal Sonic remarks "Chaos Data has been copied" after Froggy and Chocola the Chao are rescued). Big sets out to recover Froggy again with help of Amy Rose and Cream the Rabbit, thereby forming Team Rose.
In Sonic Chronicles: The Dark Brotherhood, Froggy assists Big in combat with the POW Moves "Froggy Poison" and "Froggy Rain". One of the game's side-quests involves searching Green Hill Zone for Froggy's missing frog friend, Norton.
Froggy also appears in Sonic X and has basically the same purpose as he did in Sonic Adventure. In a later episode, however, Froggy made Ella faint after jumping out of Big's fur and scaring her during a battle tournament. He is voiced by Amy Birnbaum in the English dub.
Froggy is Big the Cat's All-Star Move in Sonic & Sega All-Stars Racing. However, he appears to be very large, about 2 to 3 times larger than Big himself. Froggy will hop down the racetrack and plow down anyone in his way.