When did they stop putting VDB on the back of the penny?

They stopped putting the VDB on the back of the penny in 1909, the same year they started it. In 1918 the VDB was again placed on the cent but it is located on the obverse [heads] side along the rim at Lincoln's right shoulder. It is still there today although it can be difficult to see if the die has been used to strike a lot of coins.