The size we used for our 8 foot ceilings is 3 1/4 inches.
It must be a standard height because we bought it in bulk off the floor from HomeDepot.

We have 8' ceilings with 6" baseboard.

We have 6 inch baseboards with a 1.25 inch cap (total 7.25") and 8 foot ceilings.

5-6 inches

7 3/8 inches here.

Ours is also 3 1/4". I love beefy trim and mouldings but I think this fits our ranch with 8' ceilings.

Higher baseboards give more substance to rooms with standard 8' ceilings...particularly when paired with 2-piece crown (a beaded board base plus the profile piece). Counterintuitive, I know, but it actually makes the ceilings seem higher. But do keep your floor and ceiling trim in scale with your door and window trim...if it's narrow, keep the baseboard design very clean, and use a simple profile for crown, if you use it. You want all the trim to work together.

I think the post-war trend to narrow baseboards and trim was motivated more by the need to provide relatively inexpensive housing for a booming population than by aesthetics.

That's a good observation. Our house was built in 1950. No crown at the time, but the baseboards and window trim were good size. We've since added 5" crown to most of the rooms.

I believe it depends on the style of home you have or the look you are going for. Like NHB said, all the trim needs to work together. Do you have any photos to share?