Lead Screws and Nuts - or maybe this should be called "drive systems"
Your lead screw / lead screw nut are a very important part of your CNC machine. They are what drive the axis back and forth! The biggest issue with adrive system is backlash - backlash is basically where your nut and lead screw have some play between them - and the problem is when the computer tells the motor to turn the screw and the screw turns but the nut doesn't move (because there's a small amount of play) then the computer "thinks" the table is in a position that it's not. For an example of backlash, thread a nut onto any bolt and, without turning the nut, pull it back and forth - notice the little bit of play the nut has? That's backlash...
As will all things there are a few choices in this area too. (Pictures and animation coming soon!)
Standard threaded rod and standard nuts - you can get these at your local hardware store, you can get threaded rod in various thicknesses and lengths, it's cheap and quick, but has a high potential for backlash.
Acme Threaded Rod and Acme Nuts - Acme threaded rod has a slightly different profile than standard threaded rod, it's flatter and doesn't come to a point like it's cheaper counterpart - it's also manufactured to a slightly higher standard, which means there's generally less backlash.
Ball screws - Ball screws are a system in where there are ball bearings in the "nut" that ride along the ball screw track - basically giving you a much less backlash system - but also more expensive and harder to set up.
Rack and Pinion - While not a "screw and nut" technically, these are also used to drive a machine back and forth. In this set up a gear is attached to the motor shaft that turns and mates with a toothed rail.
Belt and Chain Drives - Again, not technically a screw and nut, but another way to drive the axis of a machine. In this scenario the motor has a sprocket or timing pulley that mates with a chain or belt and drives the axis back and forth.
In my opinion, the Acme threaded rod and nuts win this category. Acme threaded rod isn't that much more expensive than regular threaded rod and there are numerous anti-backlash solutions out there that are priced for the hobbyist.