""Standard"" length means any length that fits your desired use, unless you are talking about using them with some specific goal in mind.
A through hole header has five main dimensions. Pitch between pins, size of the pin, length of the bottom side, length of the post, and length of the top side.
The most common are 0.1" pitch, 0.025" square pins. "A" in that picture is the side that goes through your pcb. If your pcb is very thick, and A is too short, you will not be able to properly solder it. If the pcb is too thin and A is too long, you could short something out, have a lopsided board or have to cut them. "C" in that picture is the top side length. This mates with a connector. Too short and it might not be secure or might not have a good electrical connection. Too long, and the connector doesn't sit flush with the posts, so you might end up bending them.
Having just measured a ide/pata header, it is ~0.25" C with a B total length of ~0.435" (7/14th) (eyeballed/rounded). For samtec parts, this is actually A = 0.100", C = 0.230", B = 0.430". This is the general IDE/PATA standard header, and pretty much all computer headers fit this.
Personally I find those too small for breadboard or general use, longer headers are more useful (I go with slightly longer .126/.456/.230 or headers that are pretty much end up equal length on both sides of a pcb .300/.630/.230)