In Fruits Basket, a number of the Sohmas have a "curse" on them that makes them transform into whatever zodiac animal they represent. The current generation was not the first generation, so there must have been some beginning generation and some reason for it to begin. Where/when/why in-canon did this curse begin?
The curse appears to be the result of the Zodiac Legend. It is based on the real Zodiac legend, but a more detailed "true" version is outlined in Volume 22. It's quite long, but I'll post an abridged version here.
Long ago, God found a stray cat, and the two became friends. God was then inspired to send out invitations to other animals, to a banquet, so that he could meet more of them.
Twelve animals showed up (the twelve animals of the Zodiac), as well as the cat. The banquet was fantastic, until the cat collapsed on the floor, his life having finally run out. Not wanting to let go of his friendship with the cat, God forced the cat to drink an elixir of life, giving him immortality. He then had all the other twelve animals drink it as well.
As the cat came to, he told God that he did not want immortality. Everyone was shocked at the cat's rejection of immortality and his acceptance to let his life end. This allowed him to die, but the other animals didn't care, as they felt betrayed and alienated.
Eventually, the other animals were able to die as well, and God was once again left alone. As God's time to live came to an end, he accepted it, because he knew that he would see the other animals again on "the other side".
Seems like a pretty happy ending, but the way the volume tells goes on a bit after this. In particular, it says:
At what point...
... did it become a curse?
When did it change...
... into a burden?
This event appears to be the origin of the Sohma Curse, as each cursed Sohma represents one of the twelve animals (and Kyo is the cat) that met at the banquet.
It is never explained why only the Sohma clan has this curse. The only reference we have to how the curse may have begun is the zodiac story told in the later part of the manga, though it is not very clear how it relates to the Sohma or the current state of the curse.