Aberrations are another D&Dism that I have a soft spot for in some ways. It seems to be the the home for a number of creatures that are weird and alien, and... dare I say it... Lovecraftian in theme.
Sometimes all of this detail gets in its own way, of course. The gibbering mouther is an aberration. It's rather obviously based on the concept of the shoggoth from Lovecraft, yet shoggoths, when statted out (in the d20 Call of Cthulhu book and in Paizo's Bestiary) is an ooze. What? Why aren't these two creatures even the same type? Curiously, in the Paizo book, in the flavor text, it refers specifically to the mouther as being theorized to be a lesser version of a shoggoth. However, they're not even the same creature type.
In the end, I think being iconic to D&D is a great deal lesser than being iconic overall. Since the gibbering mouthers are conceptually the same as weak shoggoths, I'm going to unilaterally decide that shoggoths are also aberrations (even though they're not statted as such) and pick them as my favorite type of aberration. They're a great deal more iconic than illithids, beholders, neogi, or even aboleths (as Lovecraftian as aboleths are anyway.) So, they win.