Well, nothing was ever really stanadized for US police forces, though there have been some powerful trends that cover your sterotypical cop's sidearm very well. Right at the turn of the century you have the .38 S&W, chambered in either .38 S&W or .38 Long Colt, neither was a really powerful round, but in a simple double action revolver they worked. By the Twenties you have the .38 special, still in either a S&W or Colt DA revolver. By the fifty you'll have the S&W DA in .357, and its almost standard by the late 60's. By this time some individuals will have semi-auto sidearms. Mostly these will be the venerable Colt 1911A1 in .45 ACP, some in .38 Super in the late 70's, and the Browning Hi Power in 9mm.
By the 80s you have most departments issueing a semi-auto side arm, usually in 9mm, a Beretta or S&W being the most common. This trend continues, with the Glock and Sig weapons being added to the aray of issue sidearms. The idea was that the 9mm had plenty of power, and allowed for more rounds carried to make up for the paniced shooting under stress that many cops did when they had to use their gun. Cheap ammo most likely didn't hurt in this either.
By the mid to late 90s you have enough stories of people walking through a hail of 9mm rounds that more power is desired in a sidearm. Modern types, reluctant to go to the warhorse that is the .45 ACP went with the .40 S&W mostly. It offered more power than the 9mm, compairable mag capacity and lower felt recoil than the .45 ACP. Most of these guns are in Glock, S&W or Sig vairities. Hope that is some sort of help despite the rambling mannor in which its put up.
Kail