Four inches is what opens the sky. It gives you detail on Mars and Jupiter and Saturn, mind numbing numbers of craters on the moon, thousands of galaxies, hundreds of globs, double stars, and wide variety of dark and emission nebulae.
And it would take 80 inches to do "that much again."
So, proud as we may be of our 5" and 14" and even 20" and 30" apertures, and keenly aware as we may be of the improvements in performance, the fact is that these are all improvements at the margin compared to what the first four inches of aperture do.
well, that's almost correct. back to my earlier post, here's a chart of the relative gains in light grasp and relative reduction in the resolution limit as aperture is increased from the minimum useable to the largest practicable (affordable, physically manageable, etc.).
95% of the resolution benefit possible with the largest possible aperture is obtained with aperture that is only 20% of the maximum. in contrast, 95% of the light grasp benefit possible is only obtained with 98% of the largest possible aperture.
this concisely explains why folks interested in resolution -- double star astronomers, lunar and planetary astronomers, solar astronomers -- are perfectly content with relatively small aperture instruments that maximize luminance and frequency contrast. they are assisted by the triple inducements that their targets are inherently bright (too bright, in large apertures); the small apertures are relatively insensitive to atmospheric turbulence, yielding the maximum benefit of the resolution advantage; and the small aperture allows a relatively large range in focal ratios, emphasizing either wide field of view or increased magnification.
on the other hand, this also explains why folks interested in light grasp -- deep sky visual observers, almost exclusively -- push aperture limits as far as their pocketbooks or ability to move heavy equipment or stand on a ladder will allow. "aperture fever" is the result, which is facilitated by the very fast focal ratios that give large apertures a wide field of view and a bright image at the expense of magnification, which is less attractive due to the mirror and atmospheric turbulence that larger apertures can exacerbate.
astrophotographers are generally most interested in a flat, large image field in instruments of a size and weight that allows them to be accurately tracked or guided, which is for them also an inducement to smaller apertures: CCD sensitivity, image stacking, long exposure times can more than make up for the loss in light grasp.
this relationship is invariant whether you take the maximum practicable to be 100mm or 10 meters. to greg's suggested maximum of 30" (760mm), the 95% resolution instrument is 150mm.
instruments in the middle, between 8" to 12", try to have it both ways, and for many are successful compromises. but this obscures the fact that aperture is not a continuum of benefit but a rather sharply divided regime of competing benefits, and instruments larger or smaller than the compromise range emphasize one benefit over the other.