Why did Saruman take over the shire in The Return of the King?

Sheer spite and nastiness. Saruman wanted to get back at the Hobbits who had indirectly caused his downfall.

In The Lord of the Rings, Meriadoc Brandybuck and Peregrine Took (Merry and Pippin) were captured by Orcs who were taking them to Isengard, Saruman's castle. The Riders of Rohan intercepted the orcs and slew them all, but Merry and Pippin had escaped during the battle and fled into Fangorn Forest. In the forest, they met Treebeard, one of the oldest of the Ents.

With a little prodding from Merry and Pippin, Treebeard roused the Ents and led them to attack Isengard and destroy Saruman's fortress.

Because of this, Saruman thought that he would "get a little of his own back" and left Isengard. He traveled to the Shire and had several months in which to cause mischief and havoc.