Just stumbled across this product from Sparkfun: Z-axis tape!!
This is a double-sided conductive tape that will only conduct electricity vertically! In other words, it will not connect traces next to one another on the x or y axis, only on the z axis. This could be a dream solution if you want to do some solder-less circuit building with surface-mount components. I'm excited to try this product and will be ordering some right away.
A demo of the product by Sparkfun (begins around 1:05):