I am running Chrome 24 on OS X Mountain Lion.
I used to have Wikipedia, Youtube, etc. in "other search engines" with assigned keywords; and omnibox auto complete works fine for pages I visit on a regular basis (I am a regular maintainer of some Wikipedia pages).
For instance, say I visit a Wikipedia page titled "Foo" frequently, and my shortcut for Wikipedia is w, then typing w in the address bar will convert to Search Wikipedia, and a following f would give me an autocomplete Foo, which saves me two keystrokes (in real life autocomplete sometimes save me more than ten keystrokes; and I use that instead of bookmark since I'm a keyboard person).
However, recently I dragged Wikipedia, Youtube, and a few others from "other search engines" to "default search engines", then things changed completely. (By "dragging" I mean I first click "make default", then make Google as default again, but the effect is as if I dragged something from other to default.) Omnibox no longer offers autocomplete (or only show autocomplete after I've typed in one complete word, or even more) for these engines, no matter how many times I manually type something into it.
I wonder why is this happening? And is there any possible fix? (Well, one possible fix, I guess, is to drag them down to "other" again. However, I haven't seen any positive effect, either. You know, omnibox is supposed to be really sensitive; sometimes you mistyped an address and you end up getting the same wrong address every time with autocomplete. It makes no sense that after manually typing ten times omnibox still cannot predict your behavior.)
