Which two metals will cold-weld together in vacuum simply by touching?

Any two clean identical metals. A metal surface in air carries an oxide layer within milliseconds, and that layer is what stops two pieces bonding when you press them together. Remove the atmosphere and the oxide, and the atoms on each surface cannot tell which piece they belong to - the join happens with no heat and no filler, because there was never really a reason for two pieces to stay two pieces.

It is a genuine spacecraft problem. Hinges, latches and bearings have seized in orbit, and a Galileo antenna that failed to unfurl in 1991 is often attributed to it after the lubricant was shaken out during a long lorry journey. Designers now specify dissimilar metals, coatings and solid lubricants for anything that has to move in vacuum.

Dissimilar metals resist it because their crystal lattices do not match, so the atoms cannot fall into a shared structure - which is also why the effect is strongest between two pieces of the same metal. It is used deliberately on Earth: cold welding joins aluminium and copper conductors without the heat that would ruin nearby components, and is how some sealed electronic packages are closed.