I consider myself a run of the mill rec rider, and here are my truthful experiences with a threaded headset, featured on my '05 Bianchi Brava, the last of the truly 'classic' Bravas, if that word can be applied to a Taiwan-manufactured bike (the '06 switched to threadless for good).

The threaded headset required constant adjustment. After a crash in the middle of a ride it was knocked loose, and not knowing enough or having the proper tools to tighten it correctly I was forced to ride it loose to get back home. The threading got damaged, and pretty soon the headset was coming loose pretty much on a weekly basis, even after taking it down to the shop to get it tightened multiple times. My headset and quill stem also creaked - a lot. Every hard stroke up a hill would give me a very confidence-inspiring squeak or groan from the whole setup, even with all the bolts tightened down.

I finally received a shiny new silver headset from Bianchi under warranty, and boy did it look nice. The problems went away, but even so I was turned off of threaded headsets for good. During the three months in which I owned the Brava, there was not a one to two week period when a new headset problem arose. I gotta honestly say that I'm a lot happier with my new Veloce with threadless.

Here is the small list of advantages and disadvantages that I compiled through my experience only. Please note that most people with threaded headsets haven't experienced the problems I have and like them very much, but I'm just recounting based on my story.

Threaded
-Comes loose, requires constant adjustment
-Requires a flat 32 mm wrench to properly maintain/tighten
-Creaky (for me at least)
-Lack of stiffness
-Always a little bit of play between fork and steerer, even when tightened down

-Admittedly, looks very beautiful when done right
-Adjustable

Threadless
-Non-adjustable
-Lack of 'classic look'

-Much stiffer, tighter
-Adjustment requires minimal tools