The original bicycle chains were of a "bushingless" design, then later they came up with a roller chain design that utilized bushings, this was later updated again to the chains we are used to today that are again of a "bushingless" design.
Wikipedia says the following which I find to be incorrect as KMC's higher end chains such as the SL DLC series as well as Sram and Shimano chains are all "bushingless" and are likely the most prevalent in the industry.
With these limitations in mind, the Nevoigt brothers, of the German Diamant Bicycle Company, designed the roller chain in 1898, which uses bushings, and it is the prevalent chain today. Whether it be single rear cog (for example coaster-brake singlespeed or with an internal-gears hub), fixed-gear (such as track bikes and modern urban "fixies") or multi-speeds with derailleurs, all modern chains in use today are of the "roller chain" design. Although it is still possible to order lower cost "bushingless" chains from China today, with generally lower manufacturing costs across the board, bushingless chains are generally considered undesirable and not prevalent
Sheldon Brown also says that new chains are of a bushingless design,
The major revolution in chain design has been the introduction of the bushingless chain. The first of this type was the Sedisport (now made by SRAM), and it has acquired such a good reputation that other manufacturers have copied the design.
At what point did this most recent change to a bushingless design occur?