If you are unfamiliar with the different video connections and connectors, you should probably at least skim this first: Video Compatibility Matrix
If you want something more in-depth, here's some Wikipedia articles ranked ascending in order of quality of signal:
- RF Modulator
Composite
S-Video
Component
RGB
SCART/RGB
VGA/D-Sub
RGB/Component Sync Methods
DVI
HDMI
I am an American, so I only have firsthand experience/understanding with/of NTSC, if any of you want to contribute PAL information, I'll happily add it, but keep in mind our TVs are generally not compatible with RGB and SCART, so I will mark them best PAL and best NTSC as appropriate.
I tend to favor unmodded solutions as far as priority goes, as I like keeping my hardware virgin, but don't let that discourage you from submitting modded solutions, as they will be listed too!
Atari 2600
- Best non-modded solution: RF
Best modded solution: RGB
Second best modded solution: S-Video / S-Video
- Best non-modded solution: RF
Best modded solution: RGB VBXE Board
Second best modded solution: S-Video
- NTSC best non-modded solution: RF
PAL best non-modded solution: RGB (French 7800s only)
Best modded solution: S-Video / S-Video Alternate
- Best non-modded solution: RF
Best modded solution: S-Video
- Best non-modded solution: RF
Best modded solution: Composite
- Best non-modded solution: RF
NTSC best modded solution: Composite
PAL best modded solution: RGB (only PAL consoles)
- Best non-modded solution: RF
Best modded solution: Composite
PAL Best modded solution: RGB
- Best non-modded solution: RF
Best modded solution: VGA
Second best modded solution: RGB (later SG-1000 IIs only)
Third best modded solution: Composite
- Best non-modded solution: RF
Best modded solution: RGB
Second best modded solution: RGB (requires replacement PPU)
Third best modded solution: Composite
- Best non-modded solution: Composite
Best modded solution: RGB
Second best modded solution: RGB (requires replacement PPU)
Sega Mark III
- Best non-modded solution: Composite
Best modded solution: RGB Present in A/V, need amplification
Second best modded solution: Component (video encoder outputs component video but no mod has been found yet)
- PAL Best non-modded solution: RGB
NTSC best modded solution: S-video
- Best non-modded solution: RF
PAL Best modded solution: RGB
NTSC best modded solution: S-Video
- Best non-modded solution: RF
Best modded solution: RGB
Second best modded solution: RGB (requires replacement PPU)
Third best modded solution: S-Video
Fourth best modded solution: Composite
- Best non-modded solution: RGB
Second Best non-modded solution: S-Video
- Best non-modded solution: RGB Model 1/RGB Model 2
NTSC best modded solution: S-Video
- Best non-modded solution: Composite
Best modded solution: RGB Alternate RGB Guide in Spanish
Second best modded solution: S-Video Alternate S-Video Guide 1 Alternate S-Video Guide 2
- Best non-modded solution: S-Video
Best modded solution: RGB
- Best non-modded solution: RGB
Best modded solution: Component
Second best modded solution: S-Video
- Best non-modded solution: RGB
Second best non-modded solution: S-Video
- Best non-modded solution: RGB
- Best non-modded solution: Composite (with TurboBooster, TG-CD or custom cable)
Best modded solution: RGB/RGB
Second best modded solution: S-Video
- Best non-modded solution: Composite
Best modded solution: RGB
Second best modded solution: S-Video
- Best non-modded solution: Composite
Best modded solution: RGB
Second best modded solution: S-Video
- Best non-modded solution: S-Video
Best modded solution: RGB
- Best non-modded solution: S-Video
Best modded solution: RGB
- Best non-modded solution: RGB
Second best non-modded solution: S-Video
- Best non-modded solution: S-Video
Best modded solution: RGB
Alternate RGB Guide/RGB (certain N64s only)
- Best non-modded solution: RGB
Second best non-modded solution: S-Video
- Best non-modded solution: VGA for games that support 480p
Second best non-modded solution: RGB
Third best non-modded solution: S-Video
- Best non-modded solution: VGA via SoG/Blaze/Xploder bootdisk for games that can be forced into 480p
Second best non-modded solution: Component
Third best non-modded solution: RGB
Best modded solution: Universal VGA cable
- Best non-modded solution: Component for games that support 480p
Second best non-modded solution: S-video
PAL best non-modded solution: RGB
- Best non-modded solution: Component
Second best non-modded solution: RGB
Best modded solution: VGA Sync-On-Green Cable and modded BIOS
Xbox 360
- Best non-modded solution: HDMI
Second best non-modded solution: VGA
Third best non-modded solution: Component
- Best non-modded solution: HDMI
Second best non-modded solution: Component
Third best non-modded solution: RGB
- Best non-modded solution: Component
PAL third best non-modded solution: RGB
- Best non-modded solution: HDMI
Second best non-modded solution: Component
Third best non-modded solution: RGB
- Best non-modded solution: HDMI
Second best non-modded solution: Component
Third best non-modded solution: RGB
- Best non-modded solution: HDMI
Second best non-modded solution: Component
Third best non-modded solution: RGB
Edits
Older changes:
- Added Xbox One
- Added Playstation 4