I guess I'll add a little onto 7HCs topic of couplers, including when you need them.
You want a coupler if you are using a motor to direct drive a screw of some sort (acme, ball, etc). They allow some miss-alignment between the screw and motor to exist without destroying the bearings in your motor or in the bearing blocks supporting your screw, and without introducing much backlash. If you use a rigid coupling, and the screw and motor shaft are not _exactly_ aligned (exactly), then when you bolt everything in place, the combined screw/shaft/coupler assembly is going to "dog leg" (somethings gotta give). When your motor spins you are gonna get a "cachunkachunkachunk", which probably won't be audible at low speeds, but you bearings will feel it. You can get a sense of it if you turn the shaft by hand, you will feel the resistance increase and decrease as you turn the screw. So, long story short, if you are going to direct drive, get some couplers.
Other than the 2 types that 7HC mentioned, there is also a type called a bellows coupler. As far as cost go, they tend to go (from cheapest to most expensive) lovejoy < helical-beam < bellows, which corresponding improvements in backlash with increased price.
In most cases, if you are using stepper motors, you are going to want to direct drive. This is because steppers have a lot of low end torque, and pretty poor high speed torque. If you are going with servos, they have a higher top speed, and a lower max torque, but the torque, but the torque is more even over the rpm range. That means that with servo motors you are likely going to want to gear down with a belt system, IE, no couplers.
One case you may have a stepper motor and not want to direct drive is if you have a really heavy load, like a z axis. In this case you can get a huge motor like Steve's NEMA42, or you can get a more standard motor and gear down. You will get slower rapids in your Z, but everything is a tradeoff.
Other cases where you may be using steppers, but don't want to direct drive are if you are using a direct belt drive, such as on some 3d printers (Prusa Reprap X/Y axis). These are typically really low load situations (low torque) and high speed. Incidentally, this is also how a lot of inkjet printers work. They have a head driven by a stepper motor and a toothed belt. They typically ride against an incremental encoder, and there are home and limit switches so the thing knows where to start. Pop one open some time, and you will see what I mean, lots in common with a CNC machine.