Updated late 2017
Most HDTVs today can accept a number of different input formats. These are typically listed in the specifications as:
480i, 480P, 720P (sometimes not), 768P (mostly not), 1080i, 1080P (sometimes not) and 4K. The inputs handle the various outputs from STBs, DVD players, etc. Note that all HDTVs do not handle all formats. For example, some TVs do not accept 720P signals, 768P, or 1080P signals. When you press the Info/display/recall or similar button on your TV's remote, it's the incoming signal information that's displayed on screen. If your display doesn't show the input signal that way, often when you change inputs, it'll show the incoming signal for a few seconds.
These are the formats that the TV will accept via the various HD inputs. Please do not confuse this list of input formats with the actual display resolution.
On fixed pixel displays (most sold today) all incoming signals are converted to the native resolution for display. This will depend on the TV, but most sold today have a native resolution of 768P or 1080P or 4K. These are often listed with two numbers as outlined in bold below:
Most of the inexpensive (and older) plasmas and LCDs are 768P (1365 x 768, or 1024 x 768, etc). There are also quite a few 1080P TVs available (1920 x 1080). There are sometimes different (odd) formats, but you get the idea. There are no new 720P TVs - these are usually 768P and improperly "promoted" by sales people. Years ago there were occasional 720P HDTVs (DLPs for example)
There is a "new" format called 4K Ultra-HD. 4K UHD is a resolution of 3840 pixels × 2160 lines. These TVs have 4 times the number of pixels of a 1080P TV but 4K material is somewhat limited depending on service provider or streaming service.
Note that some HDTVs do not accept 480i via the HDMI input - typically Samsung, LG, some off-brands; while others like Sony, Panasonic, Pioneer, Hitachi will accept 480i via HDMI. This can have a (slight) impact on SD PQ when you need to set a STB to 480P instead of 480i for example for the SD channels, since most STBs are not as good at the conversion as the TV is, and there are two conversions instead of one.
The only TVs that natively display 1080i are CRT-based TVs. (There are a (rare) couple of plasmas that can "mimic" this type of display)
The SD inputs on the display, like S-video or composite video, accept 480i only, obviously, and these signals are converted to the native display format.
This upconversion from SD is handled by firmware/hardware in the TV which extrapolates and interpolates the necessary information for the final display format. The better the quality of the firmware/hardware, the better the quality of the final image. This is part of the reason why some TVs are better at displaying SD than others.
Most HDTVs seem to prefer (provide a better picture) when fed a 1080i signal instead of 720P for HD. This is generally, but not always true - try both. Since BTV changes all (HD) channel formats to 720P, the 720P setting may be better for BTV to minimize format changes.
Most TVs provide the best PQ when fed the native signal through the STB (passthrough mode for 480i, 720P, 1080i). This is not always available on all STBs and is not available on DVD players. In those cases, most HDTVs seem to prefer (provide a better picture) when fed a 1080i signal instead of 720P for HD.
Upconverting or HD-DVD players are a different matter and will likely supply a superior signal from an SD-DVD when set to one of the HD formats, usually 1080i (or P if accepted), but please experiment to see what works best for you.
Sometimes there are limitations on the various TV inputs, for example one HDMI connection may have a different input format limitation from another HDMI input, or component video input and that may be different from the PC input (which may have recommended formats/setup in the operating manual).
Please PM 57 if you have any comments or suggestions regarding this FAQ.