As much as I've tried so many different ones, I always come back to the shape of the Cinelli Giro di Talia 64 bar, 42 cm preferred. Sometimes it feels too stiff, but it just fits so well!
Campy record brake levers. I just like the way you can circle the grip with middle finger and thumb just touching and hold it lightly with total control, very comfortable. I know that the modern ergo fat brake levers seem to distribute the impacts better, but I still love the Campys.
The Huret titanium Duopar rear derailleur. Just a jewel like feel and shifting with just a little flick of the Campagnolo friction bar end. They can't be forced, but they work so well when treated well.
TA Cyclotourist cranks. Talk about vintage! Nonetheless, if you want a gear that you can't get in a standard size (half step and granny), and virtually never in stock, but a great serviceable setup.
I'm sure there are other parts I can wax ecstatic about, but I'll second a couple of other's choice. I haven't ridden tubulars for at least 20 years, but after paying $8 apiece for Clement Criterium Seta, matt tread 220's back in 1968, and riding them for a while, I told myself that I wouldn't ride anything else for the rest of my life. $47 tires in the mid 70's put a stop to that, but those tires will make any nasty bike feel wonderful.