What is CNC?

Here is how Wikipedia defines CNC:

CNC was preceded by NC (Numerically Controlled) machines, which were hard wired and their operating parameters could not be changed. NC was developed in the late 1940s and early 1950s by John T. Parsons in collaboration with the MIT Servo mechanisms Laboratory. The first CNC systems used NC style hardware, and the computer was used for the tool compensation calculations and sometimes for editing.

CAD/CAM Software:

Most CAD/CAM software is out of reach to the typical hobbyist. They typically cost thousands of dollars, but there are a few inexpensive gems out there.

Mach3
Artsoft has been in the CNC business since 2001. In this time, the Mach series of CNC software has evolved into the best available PC-based CNC software on the market. Not only is it extremely affordable to the hobbyist and industry alike, it is pioneering in it's features and continuing development. There are over 10000 users of Mach who swear by its ease of use, great features, and outstanding support.
Price: $159 [demo available]

Meshcam
MeshCAM lets you create toolpaths from your 3D files quickly and easily. No CNC experience is required- you can be cutting parts in minutes.
Price: $175

GSimple
G-Simple is a simple CAM for 3 Axis Machining Centers. 
Price: $Free

GCAM
GCAM is the GNU Computer Aided Manufacturing open source package. It currently supports any 3-Axis Computer Numerically Controlled (CNC) mill such as the Taig or Sherline in both english and metric units. GCAM consists of a simple interface for making bolt holes, drill holes, sketches, templates, and more. After extruding these entities one can export the corresponding g-code for the selected cutting tool(s).
Price: $Free

LinuxCNC
EMC2 is a software system for computer control of machine tools such as milling machines, cutting machines, robots, hexapods, etc. EMC2 is Free software released under the terms of the GNU GPL (General Public License).
Price: $Free

CodeShark Mill
CodeShark Mill is a hybrid CNC code editor with built in cad/cam/dnc functionality. Codeshark includes DNC communications, full editing, an integrated Cad system as well as a unique feature set not found in other programs. CodeShark is affordable for the individual machinists and multiple seat discounts make it economical for machine shops as well.
Price: $49.00

CNC Controllers:

Stepperworld
Introducing the FET3/Hobbyist Here's our powerful FET-3 controller bundled with NEMA 23 motors, power supply, and everything you need to get started. A complete mid-level system, at an unbeatable price!
Price: $269 Complete System

HobbyCNC PRO
Control 3 or 4 Stepper Motors From Your Computers Printer Port! Ideal For Desktop Machining and Robots! Control Routers, Lathes, Mills, PCB Drillers, and Engravers! Just About Anything!
Price: $79 [3 Axis]

linistepper
The linistepper is a well reviewed, open source controller / driver for small to medium sized 5, 6 or 8 wire unipolar (not 4 wire bi-polar) stepper motors featuring ultra smooth old school linear microstepping combined with modern active current regulation from an onboard PIC microcontroller.
Price: $90

Xylotex 
The Xylotex 3 axis drive box takes the componenets of the "3 axis system kit", mounts them in the box shown below, along with an extra cooling fan, Three 6-foot motor cables that feed out the back of the drive box to connect to the motors via Molex connectors. The cost of the complete drive box, with all cables (Motor cables, 120VAC Power cable, and the Parallel port extension cable) and the Three 269 oz.in. Double Shaft, Double Stack bipolar stepper motors (all plug & play ready-to-go)
Price: $410

Machinery: Mills, drills and routers

Sherline
Sherline mills can be retrofitted for CNC-use or they can also be ordered with stepper motor mounts factory installed. Note that Sherline provides only the mounts and couplers. The customer is responsible for completing the system with the purchase of stepper motors, drivers, a computer and software. Some prefer to build their own system from off-the-shelf parts, while some prefer to go with a package from one of our aftermarket suppliers. (See our list of CNC SUPPLIERS for details.) The Sherline stepper motor mount and coupler system assures a consistent design that is compatible with the quality of the other Sherline components for a smooth running and accurate CNC system..
Price: $880 and up

Taig
Advanced Bilevel Chopper Drive technology coupled with new 200 oz-in. stepper motors providing rapid traverse speeds of 30 inches/minute with High Motor Torque. Step resolution of 0.000125 inches. Precision Engineered Steel and Aluminum structural design. STEEL CUTTING capability with tests showing a single pass 1/8" depth slot cut in mild steel with a 1/8" end mill -Try This on other desktop mills!
Price $2155

MAXNC 10 Open Loop
Bringing the power of modern CNC machining to model engineers, machinists, hobbyist, inventors and students. Controlled from the printer port of any PC compatible computer. Build in the U. S. A. by MAXNC.
Price: $1595

CompuCarve
Compact, computer-controlled, 3-dimensional woodworking machine with an easy-to-use interface. It allows a novice to make a complete project without a shop full of tools.The unique configuration allows it to perform many other woodworking functions, including ripping, cross cutting, mitering, contouring, jointing and routing. The CompuCarve can work in most soft materials, including wood, plastics (polycarbonate or cast acrylic) and certain types of high density foam. Set includes CompuCarve machine, (1) 1/16 in. carbide carving bit, (1) 1/8 in. carbide cutting bit, CarveWright Memory Card, starter software package, (2) 1/4 in. bit adaptors, vacuum bag adaptor, bit removal tool, hex wrench, owner's manual and Quick Start Guide.
Price $1999

DIY Machines: Make it yourself and save

Easy to Build Desk Top 3 Axis CNC Milling Machine
Here is a way to make a computer controlled milling machine. That puts the real power of a computer control machining into the hands of the average human. Small enough to set on the desk but scalable to any size. As inexpensive as possible without sacraficing accuracy (too much). All most all the parts can be purchased in local retail stores. And above all CHEAP you can be up and running for well under $200. With it you can do 2 Dimentional engraving and PC board etching and 3D milling and modeling in Foam, Wood, Plastic and other soft materials.
Price: $<200

DIY Sieg
The Sieg X1 micro-mill was purchased from Harbor Freight. Stepper motors are Ebay surplus 150oz/in. NEMA 34's. Motor mounts are made from 1/2" baltic birch ply. We have a full woodworking shop at our disposal. Instead of spending several hours making nice machined aluminum motor mounts, these where put together in a few minutes. We will eventually use the cnc to mill mounts out of aluminum once everything is working to our satisfaction. The stepper drivers are our own design using LMD18245 with a 16F84 PIC doing the microstepping translation. Rapids are currently set at 15ipm @ 32,000* steps/inch. Machine can move faster but we have the gib screws really tight to limit table chatter for cutting metal. Setting the maximum rapid speed lower guarantees no missing steps.
Price: $Varies

HobbyCNC
HobbyCNC has some very reasonable plans for sale. Here are the specs on their router:

• Can Rapid Travel at Over 150 Inches per Minute With Our HCNCPRO Driver Board Package Using 127oz-in Stepper Motors at 35VDC!
  
• 9″ x 24″ x 1″ Cut Area From a 15″ x 34″ Footprint!
  
• Open Ends Allow Unlimited Stock Length
  
• Uses Dremel© Type Rotary Tool
  
• Vacuum Part Piece Hold-Down
  
• Minimum of Parts to Make Building Easier
  
• Constructed From Birch Plywood and Easy to Find Materials Using a Drill Press and Table Saw
  
• Let Your Computer Cut-Out The Parts You've Drawn In CAD

CNC Routing Machine Kit Version 1.3
Introducing the latest version 1.3. This machine is an enhancement over version 1.2 including features for enhanced rigidity and accuracy. Information and pricing for this kit can be found here. This is the enhanced expandable 2'x4' CNC machine, expandable to 4'x8'. Enhancements over the version 1.2 kit include, added options for additional lead screws for the x-axis and ability to connect the a main table (cutting surface) to the side I-beams for extra rigidity.
Price $1100+

RepRap
RepRap 1.0 "Darwin" is a rapid prototyping machine that is capable of making the majority of its own component parts. Instructions and all necessary data are available completely free under the GNU General Public Licence from this website to everyone.
Price: $Varies [MUCH less than any other 3D printer]

Keep in mind, Craigslist, ebay, and CNCZone have lots of used equipment for sale, so you might want to check there first.

Learn more about CNC

CNCZone This is the first place you should visit to learn more about CNC.
Price: $Free Membership

This is certainly not a complete list for the CNC enthusiast, but it's a great place to start your research. If you have something to add to the list, please leave it in the comments. Thanks!