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:
This is a guide perpetually in progress, I am by no means an expert, so if you feel I am wrong about any of this information, please tell me.
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
Atari 5200
- Best non-modded solution: RF
Best modded solution: RGB VBXE Board
Second best modded solution: S-Video
Atari 7800
- NTSC best non-modded solution: RF
PAL best non-modded solution: RGB (French 7800s only)
Best modded solution: S-Video / S-Video Alternate
Bally Astrocade/Professional Arcade
- Best non-modded solution: RF
Best modded solution: S-Video
ColecoVision
Emerson Arcadia 2001
- Best non-modded solution: RF
Best modded solution: Composite
Magnavox Odyssey 2
- Best non-modded solution: RF
NTSC best modded solution: Composite
PAL best modded solution: RGB (only PAL consoles)
Mattel Intellivision/Intellivision II
- Best non-modded solution: RF
Best modded solution: Composite
PAL Best modded solution: RGB
Sega SG-1000/SG-1000 II
- Best non-modded solution: RF
Best modded solution: VGA
Second best modded solution: RGB (later SG-1000 IIs only)
Third best modded solution: Composite
Famicom
- Best non-modded solution: RF
Best modded solution: RGB
Second best modded solution: RGB (requires replacement PPU)
Third best modded solution: Composite
Nintendo Entertainment System
- 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)
Sega Master System
- PAL Best non-modded solution: RGB
NTSC best modded solution: S-video
Sega Master System II
- Best non-modded solution: RF
PAL Best modded solution: RGB
NTSC best modded solution: S-Video
Nintendo Entertainment System 2
- 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
Super Nintendo Entertainment System/Super Famicom
- Best non-modded solution: RGB
Second Best non-modded solution: S-Video
Sega Genesis/Mega Drive
- Best non-modded solution: RGB Model 1/RGB Model 2
NTSC best modded solution: S-Video
Super Nintendo Entertainment System Mini/Super Famicom Jr.
- 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
Victor/Sega Wondermega
- Best non-modded solution: S-Video
Best modded solution: RGB
Neo Geo AES
- Best non-modded solution: RGB
Best modded solution: Component
Second best modded solution: S-Video
Neo Geo CD
- Best non-modded solution: RGB
Second best non-modded solution: S-Video
Atari Jaguar
- Best non-modded solution: RGB
TurboGrafx-16/PC Engine
- Best non-modded solution: Composite (with TurboBooster, TG-CD or custom cable)
Best modded solution: RGB/RGB
Second best modded solution: S-Video
TurboDuo/PC Engine Duo/Duo-R/Duo-RX
- Best non-modded solution: Composite
Best modded solution: RGB
Second best modded solution: S-Video
SuperGrafx
- Best non-modded solution: Composite
Best modded solution: RGB
Second best modded solution: S-Video
3DO
- Best non-modded solution: S-Video
Best modded solution: RGB
Amiga CD32
- Best non-modded solution: S-Video
Best modded solution: RGB
Sega Saturn
- Best non-modded solution: RGB
Second best non-modded solution: S-Video
Nintendo 64
- Best non-modded solution: S-Video
Best modded solution: RGB
Alternate RGB Guide/RGB (certain N64s only)
PlayStation
- Best non-modded solution: RGB
Second best non-modded solution: S-Video
Dreamcast
- Best non-modded solution: VGA for games that support 480p
Second best non-modded solution: RGB
Third best non-modded solution: S-Video
PlayStation 2
- 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
GameCube
- Best non-modded solution: Component for games that support 480p
Second best non-modded solution: S-video
PAL best non-modded solution: RGB
Xbox
- 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
PlayStation 3
- Best non-modded solution: HDMI
Second best non-modded solution: Component
Third best non-modded solution: RGB
Nintendo Wii
- Best non-modded solution: Component
PAL third best non-modded solution: RGB
Nintendo Wii U
- Best non-modded solution: HDMI
Second best non-modded solution: Component
Third best non-modded solution: RGB
Xbox One
- Best non-modded solution: HDMI
Second best non-modded solution: Component
Third best non-modded solution: RGB
Playstation 4
- Best non-modded solution: HDMI
Second best non-modded solution: Component
Third best non-modded solution: RGB
Edits
Older changes:
Edits for 8/5/15
- Added Xbox One
- Added Playstation 4