Newer engines benefit more from a brief warm-up. Well-used (100k+ miles, or so) are somewhat looser inside and are slightly less likely to be damaged by use when cold.
Generally any piston powered car can be safely driven once full oil pressure and circulation has been achieved, such as within 10 seconds or so. The idea is to drive reasonably gently until its warmed up to avoid excessive thermal expansion of the pistons, (which can lead to scored cylinder walls. )
Extensive warm-ups are a hold-over from the carburetor days where cars would run poorly for at least the first 30 seconds (often longer), until the exhaust-heat for the intake manifold would warm sufficiently to help heep the fuel droplets in suspension in the intake manifold.
Also, rotary engines, especially the older ones benefit from a warm up before you drive off.
Excess engine idling is apparently a bit hard on some engine camshafts, but not all. My understanding is that it's lubrication-related but I am not sure on the actual details.