Superman and Wonder Woman always had a plutonic but amicable relationship, although at times sparks flew between the pair. Both pairs on parallel planets known as Earths One and Two. On the former, beside being teammates on the Justice League, they were tempted by one of the Amazing Amazon's old foes into a courtship with the Man of Steel. This caused quite the tempest in a teapot with Kal-El and Diana's normal dancing partners, Lois Lane and Steve Trevor. Never fear, for they shook of this temporary attraction.
As for the latter dynamic duo, Kal-L and Diana didn't seem to how the same level of eros, no doubt due to having a conflict of conscious. As this was during the period of World War II, the Justice Society teammates quarreled regarding the development of an atomic weaon by their adopted land. He was for it, she was against it. Turns out, two villains... Baron Blitzkrieg and Sumo the Samuri... helped them focus on the real issue, keeping such a device out of the wrong hands. Since it detonated, the conflict between the two Socialites defused as well.
While not technically a "twice-told-tale", the end result was the same. These were key events that cemented a substantial bond between these powerful paragons of the people, as they formed a lasting friendship that endured for years to come.