Giana Sisters came out sometimes in the dark ages of 1987. It was published by RainbowArts/TimeWarp. At this time it was the best Jump n Run for the c64. It was written by Armin Gessert, who recently (2009) published a remake of the game on the DS under the name of his own firm Spellbound and sadly died in the same year.
Because the main idea and especially the first two levels were heavily borrowed from Super Mario Bros. for the NES, Nintendo was pissed pretty bad at the time. Super Mario Bros was released in 1985 in Japan and America and of course a long time later in Europe, in 1987 to be precise. And because the c64 was more widespread across Europe than the NES, the sisters were too, so some people already thought that Super Mario Bros. is a rip off from the Giana Sisters.
So Nintendo got an army of lawyers together and filed all kinds of lawsuits. After this the Giana Sisters finally disappeared from shops, but the cracker scene of these days spread the game via post all over the world and the success of the sisters was unstoppable. That's why you look here even today! And of course because it was a great game and much better than Mario Bros. and much more than just a clone, it was a game of its own. And the soundtrack by Chris Huelsbeck added to the success too! And as a tribute to the Mario Brothers Giana's sister in the 2player mode is called Maria. And even on the US version of the box of the game it is scribbled: The Brothers are History!

Why the name of the game is written Gianna Sisters in the introscene in the game (with 2 'n's) or why nintendo published the sequel on the DS after all these lawsuits will stay a secret for all eternity.