Most riders seem to think this is critical and also that it is mysterious, but really it is neither. Most "normal" lacing patterns will work well... and also a few that aren't normal.
Cross lacing is necessary for transferring torque via the rear wheel, so at least one side of the hub must be cross-laced... usually the drive side (DS). Generally a rider will be fine with only 10 crossed spokes in a rear wheel, but there are special circumstances where this could be inadequate. Many have the impression that powerful sprinters subject the rear wheel to high torque loads, but this is untrue. They put a lot of torque on the *cranks* but the torque that the rear wheel sees is inversely proportional to gear ratio. Consequently, the highest torque loads possible occur when a rider stomps with high force while in a low gear... for instance sprinting up a very steep hill in a 34/27. In this case the load on the spokes can be high enough to cause problems, and it would be better to use a fairly stout hub and cross-lace both sides. Few riders ever feel "inspired" to ride this way on a regular basis, though.
The number of crossings depends primarily on the number of spokes. As a general rule, the maximum number is ~ #holes/9... in other words if you have a 28h or 32h hub the max is 3, and on a 20h or 24h hub the max is 2. If you try to use 3x on a 24h hub the angle is too great and the spokes will probably run into the head of one next to them.
The closer the spokes are to being tangential at the hub, the smaller the tension/ detension cycle will be due to torque, so generally a hub will be laced with as many crossings as possible. In reality it doesn't make a big difference though... you can lace a 28h or 32h hub 2x if you like. The difference between a fully tangential spoking and one that is half way between that and radial (45 degrees) is only 30%. A benefit of fewer crosses is that the spokes are a little shorter which makes the effective bracing angle a little higher.
Bracing angle is important because this effects the tension balance and the lateral stability of the wheel. This presents a conundrum on the rear wheel though, since the position of the DS flange is dictated by the wide cassette, and providing clearance for the derailleur. Because of this the spacing from the center of the wheel (rim) is "stuck" being only 16-19mm from the DS flange with a 130mm dropout width. Campy hubs are in the 16-17mm range due to their wider cassettes, and Shimano/SRAM specific hubs are in the 18-19mm range. Of course you would always like to get the DS spacing as great as possible, with the practical limit being a minimal clearance between the spokes and derailleur.
The spacing on the NDS can be whatever the hub manufacturer wants. If it the same as the DS, then both sides will have the same tension. If it is twice as large... say 36mm... the NDS tension will be *half* as great as the DS. The problem here is that a high bracing angle is good because the lateral strength and stability goes up *exponentially* with the bracing angle... but low tension on the NDS could cause these spokes to go slack under high radial loads. Since the lateral stiffness of the wheel increases faster than the NDS tension drops as you increase the NDS spacing, the NDS spokes are more likely to go slack due to *lateral* loads if the NDS spacing is small. When spokes go slack the stiffness of the wheel goes way down and the chance of the dreaded "taco" is possible.
So as you can see, the trick here is to find the best compromise, and the hub manufacturers have different ideas about which is best. The builder can often influence the tension balance and bracing angles by selecting different lacing patterns. Older AC and Ritchey hubs have <30mm NDS spacing. They like to tout that this is better than the rest... but IMO, this is the worst side of things... ie lateral stability has been compromised too much in the interests of more even tension. DT hubs are on the narrow side, and the 240 Shimano/SRAM versions also being penalized on DS spacing due to having a swapable (Campy or S) freehub body. Powertap hubs also have this issue... but with their large flanges they can be laced 1x heads in on the DS to improve the DS bracing and tension balance. White Industries hubs are 18mm/36mm in S and I normally lace them radial heads-in or cross laced on the NDS, with normal cross lacing on the DS. The Alchemy hub in Shimano/SRAM is closest to perfection with 19.6/37 spacing and these will work well laced any way you like on the NDS.
I currently only lace the PT S hubs heads-in on the DS. I know that other builders have laced other hubs this way to improve the DS bracing angle... but I consider this a mixed bag and haven't tried it yet. The PT hub is ideal since the flange is so large (70mm vs 40-45mm for the DS flange on other hubs). This proportionally improves the torque transfer, so shifting most of this duty to the NDS is fine. On other hubs there is a greater chance of torque loads causing the NDS spokes to go slack. Another issue is whether or not the DS flange can take high tension with the spokes 1x or radial.
What about radial lacing? Radial lacing doesn't transfer torque well at all, but other than that the only issue is the hub. Since radial lacing pulls straight out on the hub flange, and any cracks that might develop will grow into each other, radial lacing "challenges" the flange more than cross patterns, increasing the chance that it will fail. Some manufacturers have restrictions on radial lacing and I respect this unless the customer instructs me otherwise. It is fine on front hubs though, with lower spoke counts at least.