In most databooks, the specification you're looking for is "propagation delay" and is usually found under "Switching Characteristics". The spec is usually given for a couple of different loading characteristics. If you can't quickly find the spec, go down the far-right column marked "Units" and hunt for the lines with "ns". For gates, that's about the only spec in ns. For clocked logic such as flip flops, counters and shift registers, ns is also used for things like minimum pulse width, maximum rise time, data setup and hold times and release time under "Recommended Operating Conditions" and all kinds of propagation delay specs under "Switching Characteristics".
A related specification that I used to see all the time and don't see anymore is that of the maximum risetime and falltime of the clock waveform of clocked logic. To me, it's an important specification, especially if you're interfacing digital logic to some slower analog circuits. If the risetime of a clock waveform is too slow, standard edge-triggered logic won't even "see" it. It takes Schmitt trigger inputs to resolve the slower edges.
By the way, when using the scope to measure the propagation delay, measure the time at the 50% point of BOTH waveforms -- i.e., center the waveforms on the graticule and measure at the horizontal centerline. Many digital scopes may have a time measurement function available for comparing two pulse waveforms. With others, you may have to use cursors positioned at the centerpoints to make the time measurement. Analog scopes are a lot faster to use. (That last opinion provided as a free service.)