The American Heritage Guide to Contemporary Usage and Style tells the story of just how G secured its spot in the alphabet — and how it also changed the position of where we find some of our other letters in the alphabet:

The earliest form of the Roman alphabet had no letter g. Instead, c could represent both the sound g and the sound k. The Roman letter c was in fact a development of the Greek letter gamma. This is why c, not g, still occupies the place in the Roman alphabet corresponding to gamma in the Greek alphabet, even thought the sounds of gamma and g might seem to correspond better than gamma and c from a modern point of view. In order to to make the distinction between g and k clear in writing, the Romans developed the letter g by the addition of a small stroke to c. The Greek historian Plutarch ascribes the invention of g to a Roman named Spurius Carvilius Ruga, who lived in the 3rd century BC. The new letter g was given the place corresponding to the letter z zeta in the Greek alphabet, since zeta was not used to write native Latin words. When the Romans later began to use the letter z again, it was added to the very end of the alphabet, the place it still holds today.