Wild West is the 3rd world in Plants vs. Zombies 2, and was available since the game's launch.
Wild West unsurprisingly appears to take place in the Wild West, during the mid 19th century, a time just prior to the era featured in the Lost City. It was a period of time in which the western states of the United States were first being settled by the Europeans, where there was a prominent lack of respect for the law.
In this world, there are minecart rails and minecarts on your lawn in different locations and positions, depending on the level. While nothing can be placed on a minecart rail, plants can be placed into a minecart and moved along the rail at will.