My answer in 2000 (when this thread was created) and now 26 years later would probably be the same. I’ve hit mid-40s in a road descent on a big hill in NH that was on one of my usual biking routes. I couldn’t tell you the exact speed, but I’m guessing 45-47, which was plenty fast for me.
Individual time trial stage speeds are well over 50 km/h.
The thing about bicycles is, not all of them are stable and will not wobble at very high speed.
Absolutely. You need a bicycle designed to handle that sort of speed. Not a Walmart special.
In Tour de France downhill sections, they reportedly can go at speeds as high as 65 mph. So that is a benchmark.
Fortunately, my Peugeot back in 1987 was a brand-new decently high-end road bike (for the time). And I have a Specialized Roubaix now that actually is a Tour de France model. (But I have a bit more wisdom today than at age 18 and would never dream of going that fast now. 
)
As a teenager I would try to race down large hills and use a speedometer. I don’t know what my top speed was, but I think 40-50mph. Now that I’m older and my frontal cortex is developed I realize how insane that was, esp considering the hill had curves and I wasn’t wearing a helmet.
According to Sheldon Brown, the Peugeot PX-10 [I saw one the other day!] was OK but notoriously developed a violent speed shimmy when people loaded it with baggage on a rear rack for touring.
I wonder now what model mine is. As I noted, it’s still in the basement. (I’ve been meaning to either junk it or give it away for free because I don’t have the inclination to restore a 40-year old bike.)
My trek 520 is designed for touring and is relatively stable (making it a bit less maneuverable). It is not designed for speed. I’ve hit 39 MPH. 30 is about my comfort limit going down hill unless it is quite straight. Most hills around here have curvy roads.
Brian