According to http://www.jewishencyclopedia.com/articles/4699-costume
Striped clothing is one of the striking characteristics of the Oriental male Jewish dress. This seems against the medieval principle of avoiding party-colored garments. It is not an invariable custom, but is frequent enough to deserve mention.
And according to http://www.shamash.org/lists/scj-faq/HTML/faq/11-01-03.html
Why do tallit typically have blue or black stripes? The reason why the tallis is striped is simply because that was the fashion in Greece and Rome. But this doesn't answer the question of why blue or black? Tzitzis are supposed to include a thread of blue wool in each tassle. Most believe we do not know the specific dye needed for the mitzvah. In memory of this dye, some adopted a custom to place a blue stripe on the garment itself. Others decided to add a black stripe of mourning for the lost element of the mitzvah. The black stripe gained popularity in Europe of the 15th through 19th centuries, when black-and-white clothing was more common for Jews in general. The blue stripe is now seeing a revival in the 20th and 21st centuries, but it's actually the older of the two customs. It just seems to us to be more modern. Sepharadic Jews believes the debate over what color is appropriate precludes wearing colored stripes, so they wear white stripes (or a different weave) on their talleisim. Maimonides was of the "same color as the garment" camp. For Baladi Yemenite Jewry (those Yemenite Jews that resisted the influx of Syrian customs), Maimonides is the final word on Jewish law. So, they do not wear a tallis of any particular color. One will often find an older, more traditional, Yemenite man wearing a rich blue or red tallis with matching strings. With or without stripes.