Using my own timeframes and from the American viewpoint.

Pre war:
The most influential model would have to be the Benjamin model E/F. It was without question the finest American BB gun made, especially from a performance standpoint. If was this model that really started the American boy's love affair with the pneumatic rifle. It was produced in substantial quantities and is an easy gun to find in the US. Shooting it is a real treat.

Right behind would be the BSA Improved Model D. The first true precision air rifle in America was a big hit, but very expensive. It was, just like in England, the introduction of the diabolo pellet and rifled barrel. The D was the most important pellet rifle ever made and was the beginning point of precision pellet rifles.

The best pre war rifle is the Crosman model 101. Which was a combination of the Benjamin pneumatic system married to the diablo pellet/rifled barrel of the BSA.

Post War:
The Crosman 160 has to be right up there. It served as the introduction of the CO2 Powerlet and the last version having an adjustable trigger along with the S331 sight is in a class by itself.

Any discussion of best airgun has to include the Sheridan models A/B. Like the 160, in a class entirely by themselves.

The Crosman model 1400 probably deserves an honorable mention. The 1400 was an all-out effort by Crosman to produce the finest pneumatic rifle that they were capable of producing. This was during the "Going Great Guns" era when Crosman made every effort to improve the product line; that PY Hahn was at the same time working at selling the business probably had some influence on this.

My personal favorite from this era is the lowly little Crosman model 110. I'm lazy and like small light guns. That the 110 is one of the finest of shooters doesn't hurt.

The Benjamin 312 is another honorable mention.