A character from the Super Nintendo RPG, Chrono Trigger. You find him in 600 AD. Frog uses Water magic, much like Marle, and possesses several healing spells. His Masamune (as well as his much less plot-specific sword, the Demon Hit) does twice its usual attack damage against magical enemies. In comparison to the other characters, he's probably the weakest as far as spells go, and is overshadowed as a fighter by Ayla and Crono. His ultimate spell, Frog Squash, increases in power the lower his HP is.

On to the spoilers...

Frog's real name is Glenn, and, once upon a time, he was squire to the dashing knight Sir Cyrus. Unfortunately, Cyrus was killed in battle by the evil sorcerer Magus, and Frog blamed himself for being unable to save his friend and liege. During the same battle, Magus turned Frog into an amphibian, adding insult to injury. Both the death of Cyrus and the humiliating transformation bestowed upon him by Magus left Glenn feeling lower than mud.

At first, Frog was treated like a freak when he returned to the court, but gradually he regained his sense of self worth, and played a large role in helping to unmask the evil monster who had secretly kidnapped the Queen. Later, he was revealed to be the legendary hero much whispered about throughout the kingdom, and wielded the Masamune against Magus in a battle that caused a rift in time.

Frog eventually made his peace with Cyrus during a side quest, and, depending on whether you decide to battle him in 12,000 BC or not, either revenged himself upon Magus, or showed the misunderstood wizard mercy. If you kill Magus, you can get the ending where Frog is restored to his true form, and Lucca will comment on how handsome he is.

End of the horrible, hideous spoilers

In the Japanese version, Frog's name, appropriately enough, was "Kaeru"*, which means "frog". Heh. Well, actually, it goes deeper than that, since "kaeru" can also be used as a verb meaning "to change" or "to return". His name was actually a pun. Frog was "changed" into a "frog" and sought "to return" to his old form. His given name, Glenn ("Guren" in the Japanese), was likely another pun, this time on the French "Grenouille", which also means "frog".

I can't imagine why they would pick French as the language to make a pun on Frog's real name...

Finally, here's a quick list of all the single techs Frog can perform in the game, plus their cost in magic points (MP) and their effect:

Slurp         1 MP   Heals one party member
Slurp Cut     2 MP   Hits one enemy with physical damage
Water         2 MP   Hits one enemy with water magic
Heal          2 MP   Heals all party members
Leap Slash    4 MP   Hits one enemy with physical damage
Water 2       8 MP   Hits all enemies with water magic 
Cure 2        5 MP   Heals one party member
Frog Squash  15 MP   Hits all enemies with physical damage

*Thank you to Hyena20 for your translation efforts