Over-engineering is a concept in value engineering, not aircraft design. In general, over-engineering means making the design more robust or unnecessarily complicated than necessary. In that sense, I would say that aircrafts are/were rarely over-engineered. Older aircraft were more conservative in determining the loads.
In structural design of any aircraft, the designer tries to make the aircraft safe in a number of steps:
The process followed now is pretty much the same; however, the engineers are able to determine the loads acting on the structures to a greater precision compared to the earlier times and are able to optimize the structure accordingly. The safety factor and taking of conservative material properties have not changed much.
Though one can say that, for example, making the wing spar thicker than necessary to account for unforeseen loads is good from structural point of view, it is bad from performance/weight/fuel consumption views. The problem is that if the designer knowingly pads the safety factor more than necessary, he's actually reducing the aircraft performance. As a result, over engineering (more than design or regulatory requirements) is plain bad design and is not recommended.
In short, the process haven't changed over time- it is simply that the tools have improved and more data is available for use.
There are other issues here- aircraft like F-35 Lightning II are repeatedly called over-engineered, but the point is that they were designed for the given specifications. For example, F-35 was required by design to perform the tasks of a number of aircraft and as such is having a significantly difficult engineering period.