Perhaps the most famous pair of conjoined twins was Chang and Eng Bunker (1811–1874), Chinese brothers born in Siam, now Thailand. They traveled with P.T. Barnum's circus for many years and were billed as the Siamese Twins; due to their fame and the rarity of the condition, the term came to be used as a synonym for conjoined twins, although in recent years the term has fallen out of favor and is considered a pejorative term. Chang and Eng were joined by a band of flesh, cartilage, and their shared liver at the torso. In modern times, they could have been separated easily.
If memory serves (and the margin of the second poster seems to confirm), both Chang and Eng married and fathered children -- which leads to all kinds of questions that I doubt anyone in the 19th century was impolite enough to ask.