I have a general hatred of modern, thin, flat, cheap keycaps. My favourite keycaps are the vintage super-thick doubleshot keycaps - the thicker the better. If you've got awesomely thick doubleshot keycaps, post them in this thread!
Here are some from my collection:
Kaypro II (blue keys are the thickest I've ever seen)
TRS-80 Model III
DEC VT-100 (relatively thin, except for the one on the bottom right)
WYSE WY-50 (actually, not that thick but OK for a post-84 keyboard)
TI-99/4a (early version)
The IBM Model F single piece keycap is a bit thick and sturdy, but it's not doubleshot.