i haven't been this sad about a restaurant closing since printer's row, where i had as enjoyable a dining experience as i ever had, closed a few years back.
tho i'm a lifelong chicagoan i've only been to the berghoff twice, once for a carved sandwich and a root beer in the bar and once for a sit-down meal with a beer. the bar experience was during a weekday lunch hour, and the place oozed charisma (independent of the history of the restaurant). the sit-down experience made me feel exactly how i figured i'd feel -- like the staff had been doing what they were doing for eons. i always felt about the berghoff like i do about a few other great things in the city -- i don't go there much, but it's awfully nice to know it's there.
chicago matches up with any city when it comes to great food, but in terms of restaurant institutions, the berghoff is equaled, but not exceeded. fwiw, i'd add in the institution category the walnut room, manny's, and army & lou's.