Some PS2 games have supported 16:9 (aka widescreen) and progressive scan (480p) since 2003. (According to Wikipedia Jak and Daxter: The Precursor Legacy supported widescreen in 2001. Just change the PS2 system settings to 16:9.)
Wikipedia has a partial listing of PS2 games with HD support.
Check the game's video options to be sure. Although some games have a hidden Progressive Scan option which can only be accessed by holding X and Triangle while the game is starting up
The most important things you can do to improve the clarity, color, and brightness of your PS2 games is to get component cables (if your HDTV will accept them) and optimize the HDTV using a THX certified DVD/BluRay.
The PS2 also supports ED & HD with higher end connections like Component cables, which offer much better video quality than the standard composite & S-video cables. Be sure to check what inputs your TV can accept before rushing out to buy new cables.
Composite Cables Edit
Composite cables have three RCA plugs. Red and white for audio. Yellow for video. All three color signals are mixed over the yellow plug, which loses a lot of signal quality. If at all possible use S-video or component cables instead.
S-video isn't quite as good as component, but is still vastly better than composite. Progressive scan isn't supported over S-video cables, either. Be sure your TV has S-video inputs before purchasing an S-video cable.
Component cables have 5 or 3 RCA plugs. Red and white for audio, and Red, Green, and Blue for video. The most common problem is plugging into the wrong inputs. Either the Red video into the Red audio (and vice versa) , or the Green Video into the Blue input (and vice versa).
On the other hand, a lot of older HDTVs won't display PS1 games over component input. PS2 games that output 240p via component may not be displayed either. A quick and dirty solution is to keep the original composite cables plugged into the TV, with the other end near the PS2. Then just swap cables when switching to a PS1 game. This will also blur some of the worst jagged edges and pixelation PS1 games are prone to on HDTVs. ("Pixels the size of chickens!")
Known PS2 Games That Use 240p Resolution Edit
(and might not be displayed by a HDTV over component cables)
- Gradius III
- MegaMan X Collection
- NeoGeo (compilations, at least some of them)
- Tekken V (just the Tekken 1 & 2 arcade modes)
- WWE Smackdown Shut Your Mouth (just the opening & unlockable videos; wait 90 seconds and the main menu will appear) 
- Shadow of Destiny (Menus are in 480i)
Changing The Component Video Out Blind Edit
There are two settings for Component Video Out: RGB and Y Cb/Pb Cr/Pr.
Y Cb/Pb Cr/Pr is for USA standard NTSC televisions.
RGB is for European PAL TVs.
If your PS2 is set the wrong way then your TV won't display over component cables. You can revert to the original composite cables for long enough to make the change, or use the following procedure to make the change blind.
- Turn the PS2 on with no disk.
- Wait 10-20 seconds.
- Press Down on the D-pad once to go to System Configuration.
- Press X to select System Configuration.
- Press D-pad Down three times.
- Press X to activate Component Video Out.
- Press D-pad Right to toggle between RGB and YPbCr.
- Press X to activate the new setting. It should take effect immediately.
Cable Quality Edit
Cable quality matters with S-video and Component cables, although their superior design can compensate some for poor material and workmanship. Official Sony component cables are the most reliable, but you'll have to get Sony PS3 component cables as they are no longer manufactured for the PS2. The Sony PS3 component cable packaging states they are fully compatible with the PS2. Multi-system or universal cables can also have degraded video due to their many extra connections. Gold plated connectors will guarantee that the signal does not degrade over time due to corrosion.
Comparison of Cable Types Edit
FiringSquad.com once featured an in-depth article about the PS2's various video cable options, including Composite/S-video comparison photos, which rated the connections as follows: 
- RF connector - 2.5
- Composite - 10
- Monster Gamelink 200 - 15
- S-Video - 80
- Monster Gamelink 300 - 85
- Component - 90
- Monster Gamelink 400 - 95
HDMI Converter Edit
On eBay, and elsewhere, you can find "PS2-to-HDMI" converters/adapters,  which replace the PS2's A/V output with an HDMI output. The adapter is powered by a small USB wire connected from the device to a USB port on the front of the PS2. The product upscales the PS2's audio/video output to 1080p over an HDMI cable, though the quality is virtually no different than Component cables. In fact, just like Component cables, it can not display PS1 games (and the select PS2 games) that run in 240p.
By converting the PS2's video signal directly from the output port, with no intervening cable and connections, this box could offer improved performance as it has no analog cable runs. (Analog signals lose fidelity over cable runs and at connections. This is why the phone company engineers invented graphic equalizers all these years ago, to compensate for the losses/distortion accompanying cable runs.)
This may also work for playing PS2 games on PC monitors with the correct adapters, but again we have no direct reports.
When you change the aspect ratio of the game to widescreen, your TV does not automatically adjust. You've have to manually switch the TV to 16:9 (aka Full Screen). Don't forget to change back when you play a game in 4:3 mode.
Some games, like Ratchet and Clank 2: Going Commando, have a widescreen mode takes the easy way out and just chops off a lot of the top and bottom of the video to make it fit the 16:9 aspect ratio. Be sure to check any game you suspect this of. I preferred how the game looked in 4:3 mode. I still set the TV to Full Screen. There's some distortion, but not enough to bother me.
Progressive Scan Edit
Progressive scan is only possible over component cables. Progressive scan, or 480p, avoids interlacing and comb effects, and offers a much cleaner image for the SDTV & HDTV to display. Text and motion should be most improved by progressive scan.
The main drawbacks to improved video quality via better cables and HDTV are jagged edges and graphical artifacts becoming much more apparent. PS2 games were designed for the brighter, more saturated look of cathode ray tube televisions, not the clearer, sharper but less rich LCD screens. Some tweaking of the TVs settings can help here. First, most if not all HDTVs store separate video settings for each input. So changing the brightness on the component input won't ruin the cable TV settings.
HD Resolution Edit
1080i resolution is possible for games that support it, such as Grand Turismo 4 and Tourist Trophy. Component cables are required.
Playing on a Backwards Compatible PS3 Edit
Only the original 20, 60 & 80 GB PS3s have PS2 backwards compatibility.
External De-Interlacers, Upscalers, Smoothers Edit
You may want to consider an external option, such as those listed at at Hazard City. HD Box Pro seems to be the mid-range winner on price/performance, though mre expensive options are discussed. These may be suitable for playing PS1 and PS2 games on a computer monitor.
HDTV Settings For PlayStation 1 Games on a PlayStation 2Edit
Hidden Setting to Smooth PS1 Textures Edit
There's a hidden setting in the PS2 system browser to smooth PS1 textures.
With Browser highlighted, press Triangle.
- With PlayStation ® Driver highlighted, press Triangle.
- Press Down-Arrow once to highlight Texture Mapping.
- Press X to bring up the dropdown menu.
- Press Down-Arrow once to highlight Smooth.
- Press X to select Smooth.
- Press O repeatedly until you're back at the main Browser menu.
- You'll have to make the change every time you reboot the console.
Fine-Tuning Your HDTV For PS1 Games Edit
- Turn the TV's Sharpness setting down to 0 or 1.
- You might turn the Contrast down a little as well.
- Switching back to composite cables for the PS1 games will blur the worst pixelation, along with everything else.
- LCD screens don't have the saturation or luminance of the CRT TVs that PS1 games were designed to be played on.
- Tweaking Color up a little will help make up for that.
- For the same reason, try turning Brightness down a little.
- Playing the games in Full Screen mode will reduce detail some through stretching. Extensive testing showed the distortion wasn't significant. People and things that looked wide in Full Screen looked wide in 4:3 mode as well. Some players disagree strongly, and feel that 4:3 games should always be played in 4:3 mode.
- Some HDTVs have a 1:1 Aspect Mode setting, where it displays the video feed without upscaling. This has the same result as sitting further away, and prevents any processing artifacts.