Those old British film capacitors with the dipped color codes/bands.
Lots of vacuum tubes (see above). RK707 is a neat one:

Tim
Those "Radiation tolerant" ICs are usually quite good (and odd) looking:

and
Nixie Tubes

STC used to make those in Devon in the UK (Torbay) - I built the test gear for them in @ 1967.
Liquorice Allsort polyester capacitors. I used to have loads of these, made by Mullard (later Philips).
I can't believe no one has posted the most obvious...
I can't believe no one has posted the most obvious...

Depends on the judging criteria - Cool component, yes. Coolest looking component, no.
Microscopic led's, both visual, and convert surrounding heat into light, cooling down the surroundings
This is easy... They are all beautiful, this is why we are here. You dont have to go fancy:


Or anything high voltage or high frequency:
This is technically a vacuum tube, for a cyclotron. Does it count?

These aren't particular outstanding components, I just like the way the guy did the images.
