DVI - Digital Visual Interface, connection for Computers, Monitor Displays, HDTV, DVD

DVI - Digital Visual Interface, connection for Computers, Monitor Displays, HDTV's and Home Theater Components
DVI is a Combination Digital and Analog Video interface. Both portions of the signal are optional, so it can be only digital or only analog. DVI-D is digital, DVI-A is analog and DVI-I is an interface with both capabilities. Of course, being able to support both does not mean it will support both at the same time, DVI-I connections will only use analog or digital, not both. Normally, DVI-I will detect and choose the analog or digital portion of the interface depending on what the connected Display tells it to do.
Choosing a cable? If the connection is DVI to DVI you should use a single or dual link DVI-D cable depending on your resolution. Single link supports up to 1920x1200@60Hz. For Higher resolutions you need a dual link cable. For DVI to VGA you only need analog video: DVI-A.
Not sure what you need? See our DVI Info Page with Pictures and Descriptions of the DVI Connector Types and Cables
Home Theater Related: Home Theater Connection Guide
Good Info on HDMI to DVI:

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About DVI connectors
A DVI connection can be one of three types - DVI-I, DVI-D or DVI-A. DVI-I:
DVI-I contains both the digital and analog connections, (DVI-D + DVI-A) , it's essentially a combination of DVI-D and DVI-A cables within one cable. Note that the analog signal is VGA and can be split out with an adapter on a true DVI-I cable. DVI-I sources communicate with the display to decide on the preferred output for the monitor. It will not not send both signals. So , if you want to use Digital Video DVI-D is all you need.
DVI-D: DVI-D (like HDMI, DFP or P&D-D (EVC)) is a digital only connection. If both devices being connected support a Digital DVI connection (DVI-I or DVI-D compatible) and are compatible in resolutions, refresh rates and sync, using a DVI-D cable will ensure that you are using a digital connection rather than an analog connection, without playing around with any settings.
DVI-A: DVI-A in cable form is really rare. It is basically a VGA Cable with DVI connectors on both ends. Why use a DVI connector when you can use a cheaper VGA connector? On the other hand, a DVI to VGA cable is , in reality DVI-A to VGA Cable.

High end Cables? Who needs them?
You need them for long lengths or high resolutions. For general PC use at resolutions of up to 1680x1050, or even 1920x1200, short lengths standard cable will often do fine. At longer lengths a better quality cable is recommended. For Dual link, a high quality Dual link cable is recommended. Length issues are not just cable based, but are extremely dependant on "source" (player or cable/Satellite box) and "Sink" (signal receiving device , like TV) for results.
"Since it is Digital, Quality does not make a difference": This is false. DVI does not have any error correction. While you can get away with less quality cables for short lengths, lower quality cables will have an increasing effect on the signal errors as the length increases. Since the quality of implementation of DVI transmitters and receivers varies widely in equipment, the best reasonably priced cable should be used, to ensure the best possible video quality.

For DVI to VGA connections you can throw out all of the Digital signal length problems. You do need to rely on the cables analog Coax cable properties. Often this aspect of quality is very much an afterthought for DVI-I cables and it's best to stick with an HD quality VGA cable with a VGA to DVI Adapter.

Dual Link? Single Link? Which do I need?
Dual Link DVI - Dual Link DVI supports resolutions up to WQXGA (2560 × 1600 @ 60 Hz), but is limited to high-end computer monitors, like Apple or Dell. While Single Link DVI supports resolutions up to WUXGA (1920 × 1200 @ 60 Hz), and applies to 90% of current computer monitors and all older HDTV's.
For high resolution and high refresh rate Displays at anything other than fairly short lengths (over 10 feet) we highly recommend using the best DVI Dual Link or Single Link cable.
Very long lengths may require a booster/Equalizer for best results, or even a CAT5 or Fiber Optic Cable Solution.