The "Techelet" was a bluish color, obtained from the fluid of a sea creature called the "Chilazon." (Tosefta Menachot 9:6) It is found on the coast of Northern Israel, though here is a disagreement among scholars regarding what the "chilazon" actually is. Some say that it is a snail, while others say it is a squid. There are some who claim that the "chilazon" is actually a mollusk.
At any rate, this particular dye was very precious and because of its value, the Romans (who conquered Israel in 63 BCE) seized control of its usage. This caused the Jewish dyers to go underground. By 639 CE at the time of the Arab conquest, the secret of Techelet was lost all together.
As a commermoration of the blue thread, blue stripes were added to the Tallit itself. These later morphed into black stripes.
So while there is an origin to this custom, there is no halachic legal requirement to have any stripes on the Tallit, and if someone does choose to have stripes, they can be of any color(s). However, keep in mind that the current custom of black stripes is keeping within the synagogue decorum, which has value in and of itself.
With blessings from Jerusalem,
Rabbi Shraga Simmons