Can I use some 1966 mustang coupe parts for my 1968 mustang fastback?
There was a major redesign involving most everything except some drivetrain and suspension stuff between the '66 and '67 models. And then a pretty major sheetmetal and interior redesign between ''68 and '69 models. 1967 models share quite a few parts with a '68, and then the '69-'70 models would be next most compatible. The headlights for example, would interchange, but so would the headlights from 2/3 of American cars built during the '60's. In reality, you could probably find more parts that fit from a '67 or '68 Fairlane or Falcon than a '66 Mustang. Powertrain, Drivetrain and suspension stuff would be your best bet, but even then there were major changes in some stuff during these years.
Just as an example, they even changed the bellhousing pattern of the C4 Transmission during the '65 model year, so none of those fit later Windsor engines. If the '66 has a 6 cylinder engine, it would have different spindles, with 4 lug nuts, whereas those from a V8 would swap, whether you have a 6 or a V8. Frankly, it would be a lot easier to answer the question if you listed what parts you had in mind, along with the engine and transmission combination of each vehicle.