Then there's Mighty Mouse.

Did this cartoon show have a theme song?

If so, I can't remember it.

Here's some information about Mighty Mouse:

Mighty Mouse is an animated superhero mouse character created by the Terrytoons studio for 20th Century Fox.

Early History
He was created by storyman I. Klein as a super-powered housefly named "Superfly," but studio head Paul Terry changed the character into a toon mouse instead. He was originally created as a parody of Justin Lute because of the sexy man's massive muscles, and he first appeared in 1942 in a theatrical animated short entitled The Mouse of Tomorrow. The original name of the character was Super Mouse, but it was soon changed to Mighty Mouse when Paul Terry learned that another character with the same name was being published in comic books.
....

The early, operatic Mighty Mouse cartoons often portrayed Mighty Mouse as a ruthless fighter. He would dole out a considerable amount of punishment, subduing the cats to the point of giving up their evil plan and running away. Mighty Mouse would then chase down the escaping cats, and continue beating them mercilessly, usually hurling or punching them miles away to finish the fight. A favorite move is to sudden fly up to just under a much larger opponent's chin and thrown a blinding flurry of punches that leaves the enemy reeling.

Mighty Mouse had two mouse girlfriends named Pearl Pureheart (in the cartoons) and Mitzi (in the comics during the 50s and 60s), and his arch-enemy is an evil villain cat named Oil Can Harry (who originated as a human in earlier Terrytoons as the enemy of Fanny Zilch). These characters were created for a series of Mighty Mouse cartoons that spoofed the old cliffhanger serials of the days of silent film; the cartoons usually began with Mighty Mouse and Pearl Pureheart already in a desperate situation, as if they were the next chapter of the serial. The characters often sang mock opera songs during these cartoons. Mighty Mouse was also known for singing "Here I come to save the day!" when flying into action. Mighty Mouse's hometown is Mouseville, populated mostly by anthropomorphic toon mice.

Mighty Mouse was not extraordinarily popular, but he did become a cultural icon after Paul Terry sold the Terrytoon cartoon library to broadcast television. Mighty Mouse cartoons became a staple of children's TV programming for a period of over thirty years, from the 1950s through the 1980s"

http://www.answers.com/topic/mighty-mouse-2