As for the Tower of Pisa’s tilt, Wikipedia is explicit on the cause: an inadequate foundation on ground too soft on one side to properly support the structure’s weight. The theory of the intentional tilt seems to be as crazy as you might think.
Some of the guidebooks’ confusion, however, might be attributed to the fact that construction of the tower occurred in three stages. Work began in 1173 and the tower began to sink by the time work had reached the second floor, five years later, due to an insufficiently deep foundation and weak, unstable subsoil. Construction stopped for almost a century, because of non-stop war between Pisa and its competing neighbors.
Then, in 1272, construction resumed, with the engineers attempting to compensate for the tilt by increasing the height of the upper floors on the low side, giving the tower a slight curve. Wikipedia doesn’t mention the daftness of the solution, since the added height would have also added weight, thus furthering the sinking. After twelve years, war again intervened, stopping work at the sixth floor.
Finally, in 1319, the seventh floor was completed and the bell-chamber, in 1372, almost 200 years after the Tower was begun. However, the Tower’s tilt continued to increase.
In 1964, the Italian government put out a bid for help in preventing the Tower’s collapse — while keeping the tilt for its tourism potential. The multinational team’s suggestions included stabilizing the tower with 800 tons of lead counterweights on the raised end of the base.
Twenty years of studies later, the Tower was closed to the public, the bells were removed, and cables were attached to give support while soil was removed from below the high end in order to reduce the tilt to a safer angle. Ten more years of reconstruction and the tower was reopened to the public in 2001 and declared stable, at a tilt of 12’10” off vertical at the highest point.
Then, another 70 metric tons of subsoil were removed and in 2008, engineers announced that the Tower had stopped moving for the first time in its history.