WARNING - this page is for information only - don't worry if you don't know or don't care about your lacing pattern, we can help you out with a recommendation for the wheel build you have chosen!
Inherently related, spoke count and lacing pattern affect the ride, strength and looks of your wheel. Do bear in mind the rim you have chosen, as a strong, stiff rim can get away with less spokes than a particularly light rim where you may want to compensate for less strength with a higher spoke count.
Mountain bikes are more limited in the lacing patterns, with disk brakes placing more force through the hub, and usually 32 spokes per wheel. A three cross pattern is normally recommended, although others can sometimes be done.
Road wheels - two or three cross are still probably the best options for strength and durability of the components and the wheel as a whole, but lower spoke counts and larger flanges on the hub make other lacing patterns suitable. Not putting braking force through the wheels opens up the options for other lacing patterns as well. There is a small weight and aerodynamic advantage to be gained from using patterns which have shorter and fewer spokes.
There is a lot of accepted wisdom in the field of lacing patterns, some of it right and some wrong, while still more opinions are correct in theory but irrelevant in practice. These are our opinions based on our experience both riding and building wheels.
Three cross lacing - both sides
The classic lacing pattern, for maximum strength and durability on both road and off-road wheels (for spoke counts of 28, 32 or 36).
Not suitable for: wheels where three cross would cause the spokes to cross the heads of other spokes or where the angle of entry into the rim is too severe. This applies to 24h or less builds, very large hub flanges (including hub gears) or deep section rims.
Two cross both sides
Practically, there is little difference between 2x and 3x, and a 24 spoke wheel laced 2x is similar to a 32h laced 3x in that it has pairs of reasonably parallel spokes about 180 degrees apart to provide maximum torque transfer to the rim. At JRA we think 2x looks nicer than 3x on some road wheels. Other than that, there's not a lot of difference.
Radial lacing both sides
Radial lacing on both sides is for front rim brake wheels only. Radially laced spokes are incapable of transferring any braking or driving force from the hub to the rim.
Not suitable for: mountain bikes with disk rotors. Many hubs are not recommended for use with radial lacing as it puts extreme force on the flanges, which may break off. Royce Engineering also forbid radial lacing on their lightweight hubs because the stretching force affects how the bearings seat. This probably applies to all hubs in some way, but affects very light hubs more than chunkier ones.
The benefits: largely cosmetic, some people prefer the look of radial spoking. The spokes are also generally about 20mm shorter than for a 2- or 3-cross pattern, making them lighter and possibly more aerodynamic. The wheel should also be marginally stronger laterally (side-to-side) because of the shorter spoke and larger angle between hub and rim. These performance advantages are marginal at best.
The disadvantages: increased hub load over crossed patterns may cause failures or bearing problems (in practice we have not seen any bearing problems on the hubs we most commonly lace radially which are Chris King R45, American Classic Micro 58, and DT Swiss 240/190/180. All these hubs are approved for radial lacing). Radial lacing also produce a harsher ride over rough terrain - it's not recommended for cyclocross wheels.
Mixed radial / crossed lacing
Rear road wheels are often built with radial spokes on the non-drive side, and crossed (2 or 3) on the drive side. The drive side crossed spokes transfer power to the rim; the radial non-drive spokes don't. In theory it would probably be better to build a dished wheel (ie, almost any geared wheel as opposed to singlespeed) with radial drive side spokes and crossed non-drive. This would gain the lateral strength advantages of the radial spokes, but would require the drive torque to be transferred through the hub shell and we don't know if this is OK long-term. It will probably depend on the hub.
mixed lacing on wheelsets
This fixed wheelset uses some different lacing patterns front and rear.