Some ships I'm personally completely unfamiliar with from the transitional era after WW2 and before the mid-70s or so when we're fully into the missile age.
USS Norfolk DL-1 destroyer leader (class of 1). Extremely large for a destroyer at the time (540 feet long, over 5000 tons displacement puts around a Dido-class AA cruiser in size, displacement, and complement (over 500). Wikipedia says she was built on a 'light cruiser hull' which I assume means Atlanta family since it's a lot smaller than a Cleveland or successor.
I assume that had she stayed in service to the 1975 reclassification, she might have gotten a cruiser designation like the rest of the DLGs
USS Mitscher first in a class of 4 in her original configuration. Also getting close to the length of modern destroyers (493 ft) and much heavier than WW2 DDs (~5000 tonnes). Eventually two of the class (USS Mitscher and USS John S. McCain) were refit as DDGs with a single arm launcher for Tartar missiles
After refit in 1975
The Forrest Sherman-class were smaller and lighter (418 ft. 4000 tons full load) and like the Spruance-class seemed to lead to a bunch of experimental fits. They served all the way up to nearly the end of the Cold War
USS Decatur (DDG-31) after conversion to a DDG with a Mk. 13 launcher replacing one of the aft guns (one of four converted this way)
USS Barry (DD-933) with the same gun replaced with ASROC (8 conversions as the Barry-subclass)
USS Forrest Sherman (DD-931) keeping the gun in X position
Charles F. Adams-class designed from the outset to be DDGs as a development of the Forrest Shermans
The German museum ship Mölders. Not decommissioned until 2003 and had by then be refit with a pair of RAM launchers
Australia also operated the type
HMAS Hobart
HMAS Perth and HMAS Brisbane
One of the earlier ships in the class, USS Henry B. Wilson. Later ships switched to a single-arm launcher
British Whitby-class frigate in Amsterdam in 1969. In service from 1956 to 1974 and seemingly never fitted with missiles