It is currently estimated that around 10-20% of people paying for High Definition TV, and have a TV that could support High Definition, are still not actually watching any HD programming because their equipment is not correctly connected. What's odd, of course, is they haven't really noticed the difference. I would imagine that there is some amount of placebo effect – you are paying for HDTV, so it would be horrible to admit that you're not actually watching HDTV. On some level, perhaps some of our 10-20% know that there is something not quite right, but they don't know how to express it or they don't have any basis for comparison.
It doesn't help that between the switch to digital television, several format wars, and no less than six ways to hook up a television to a signal, the average TV watcher isn't really sure what the right way to connect the equipment is. Also, with the wide variety of devices out there, it's hard for the average person to know what the best way to hook them to their TV.
Coax – When we think of cable, as in cable TV, this is usually what we're talking about. This is the most common way that we get TV signals around in the analog world, but that's not to say that we can't get a digital signal through it. If you plug a coax cable into a device with a coax input, there's no guarantee that you'll get a visible signal, because the device you're plugging into has to be able to correctly decode the incoming signal. It's the proverbial box of chocolates, you never know what you're going to get.
Composite Video – This is an RCA connector, usually marked with a yellow connector body or a yellow strip around the connector body. This is the lowest tier of analog video. I remember that this one is the single video cable because a 'composite' is something that is formed from more than one ingredient and the ingredients remain distinct. In this case, the ingredients are the brightness signal and two signals of color information all multiplexed together into a single signal. (You don't need three signals of color information because you can figure out the third signal of color from knowing the brightness and the other two color signals.) In decoding these signals from each other, there's a small amount of inaccuracy which mostly occurs in sharp transitions from one color to another or from light to dark. We perceive this as softer edges when we're viewing a video processed this way.
If you're watching something on a VHS tape, this is as good as it's going to get. A better cable won't help.
S-Video – This is a 4-pin mini DIN connector – if you didn't know it was supposed to be plugged in a television, you might think it was for a PC mouse or keyboard. (Pro Tip – Don't try it, you'll bend the pins.) This is a little better than composite video, because the brightness signal has been separated from the two color signals. It's a little sharper than composite because the brightness is separated out, but the TV still has to decode the color signals from each other. This is mostly found on larger analog TV's and older DVD players - although some of you may remember the awesome Commodore monitors that were small TVs that supported S-Video.
Component Video - Technically this should be called 'YPbPr video', but I've never heard anybody actually call them 'Yipper' cables and it would take somebody a lot more pedantic than me to call it something that strange. I do see 'YPbPr' marked on the jacks on TV's and DVD players. These are RCA connectors, just like the composite video cables, but they're marked with Green (Y) Blue (Pb) and Red (Pr) This is one step farther than S-Video. The brightness signal gets its own cable, and the two color signals also both get their own cables.
It is not until you get to this point that you can really expect anything like an HD signal making it to your TV, but as always, consider the source. If you have a Wii or one of the previous generation consoles (Xbox, PlayStation 2, or GameCube ), and a TV with a component video input, getting the console-specific component video cables will insure that you can get the best picture possible. One caveat - GameCubes manufactured after May 2004 were made without the output jack marked "Digital AV Out" and thereby cannot have component video cables connected to them. Nintendo made it so you had to buy the component video cable from them directly instead of making it available in stores, and then wondered why hardly anybody bought them, so they stopped making GameCubes that could output better video.
DVI - This stands for Digital Video Interface, and the likely place to see this is on a computer video card. There are a couple of different versions of this connector, but it's hard to tell them apart without counting all the pins on the end of the connector. The connector body is the same in all cases, it's just not all of them have all of the pins connected. It's a large connector, almost as big as the old 36-pin parallel connectors that printers had before USB. Some early cable boxes had this, presumably so you could show off your brand new digital cable on a LCD computer screen. If you are connecting a computer to a large flat screen display, DVI is the way to go - but if the display only has HDMI inputs, it is possible to convert a DVI signal into an HDMI signal - but just the video part, of course. You probably will want to know your display's native resolution before you try to hook it up - if you're not sure what that means, ask questions before buying cables.
HDMI - HDMI stands for High-Definition Multimedia Interface. It's been designed to support a wide variety of video modes, and even allows devices hooked up via HDMI to communicate with one another for the purposes of detecting the correct video mode to display. If you have it available, use it. It also supports multichannel audio, but since I'm trying to keep the focus of this on video, we will save that discussion for later. Some newer DVD players use this connector, and most Blu-Ray devices and HD cable boxes use this connector.
Whew. I managed to make it all this way without using any of the video mode descriptors, but now I must explain them. The first two words I need to explain are interlaced and progressive.
A standard-definition TV picture as it is currently broadcast has 480 lines of visible resolution. Imagine 480 lines drawn horizontally across your TV screen, each one below the next. We'll call the line at the top of the screen "1" and the line at the bottom of the screen "480". Most television signals are 30 frames per second, so that's 30 pictures per second of TV, but the way that it is drawn is not 30 pictures in a row, one every 30th of a second. What happens is that all of the even lines of the first picture are drawn in the first 60th of a second (so that's line 2,4,6,8, etc. all the way to 480) and then all the odd lines of the first picture (1,3,5,7,...479) are drawn in the second 60th of a second. Then all the even lines of the second picture, then the odd lines of the second picture, and so on. This is called 480i. The '480' represents the 480 lines of resolution, and the 'i' lets us know that we're talking about interlaced video.
Alternately, there are video modes where all of the lines of the picture are drawn in a single pass. Your computer monitor does this, whether it is CRT or LCD or something else. The advantage of this is that contours drawn on the screen tend to look less flickery or less jagged. In interlaced video, a sharp line horizontally across the screen may seem to flicker up and down slightly, a diagonal line may look slightly jagged, and a vertical line might look ghostly. With the entire frame drawn at one time, these effects are reduced. Once you start watching DVDs in a progressive video mode, you might actually be able to read the credits instead of squinting at all of the blurry white letters on a black background! With DVD players that support progressive scan, you will have to use either the component video connectors or HDMI connection (if available), and then enable that feature in your DVD player's menu. This output will be 480p. 480 lines of resolution, and progressive scan output which means every line of video is drawn in a single pass. This, by the way, is still not HDTV. They give 480p a little bit of a break and call it 'EDTV'. The 'E' stands for 'Enhanced' - you can make up your own pharmaceutical joke here if you'd like.
If you're paying for HDTV, you're going to see that some of the HD channels are 720p, and some stations are 1080i. The nomenclature is the same - lines of resolution, and then an 'i' or 'p' to indicate whether it's interlaced or progressive scan. Of the two resolutions, 720p is better suited to fast-moving action like a football game, and 1080i is better suited to fancy-pants nature programming where the images don't change quickly and the camera pans slowly across the breathtaking landscape while Sigourney Weaver narrates.
Since the electronics industry can't leave well enough alone, they had to go and make the Blu-ray video format, which is best viewed on a TV capable of 1080p.
So, to categorize -
Standard-definition TV, VHS, older game consoles.
Connects with coax, composite video, or sometimes S-Video.
DVD players, Wii, GameCube, PlayStation 2 (but not all games), Xbox (all games)
Connects with component video cables.
Sports HDTV, Some Blu-ray movies, Most PS3 and Xbox 360 games
Connects with component video cables or HDMI
Connects with component video cables or HDMI
Blu-ray movies, some PS3 and Xbox 360 games
Connects with HDMI
Any higher resolution than 1080p, for now, assume that it will also connect with HDMI. Also, bear in mind that HDMI and component video can do lower resolutions, but they're overkill. Also, PS3 and Xbox 360 can display 1080i resolution, but most games are natively in 720p and would be rescaled slightly to display 1080i. While this is a long and involved post, I have not covered every possible scenario by a long shot. My intent is to cover the more common configurations.
And to recap - if you're not using HDMI, you might not be getting HDTV. If you don't know, have a look. If you can't tell what you're looking at, I hope you have enough information to ask the right questions now.