Impressive Paula (Amiga) Music
Being a sample-based chip, it reads waveforms from chip RAM rather than generating them directly. You could get past the 4 channel limit with software tricks (Turrican 2's title and intro tracks use 7 and so does Hoi's intro track, OctaMED tracker songs could use up to 8 but from what I've read it was a struggle to increase the channels to just 6 or 7 for an actual game while maintaining the same sound quality). One rarely used trick (Motorola Invaders 2) was to re-sample several channel tracks into one channel to give the illusion of using more channels, more akin to streaming a full song like in later Neo Geo games.
One technique that was sometimes used (for example in Toki, Battle Squadron, Hybris, Ambermoon, Bionic Commando and in tracker mods) and which gave birth to a style of Amiga music known as chipmod music to some (today it could be classified as fakebit), was to play small, single-cycle waveform samples of chiptune sounds to get C64 style waveforms, either combined with more realistic sampled drums like in other Amiga music, or sampled C64 style noise drums. This approach to Amiga music became popular in the demo scene (basically the indie scene of the period) in part because it greatly reduced the file size of each song. A trick that was eventually added to this style was to rewrite an instrument's waveform while it plays (sample offset?) to give it more character.
I don't think the C64's ring modulation and filter effects could be used for these tracks other than via sampling, but the Amiga does let you combine two channels for a 14-bit waveform, or to modulate one channel with another one as described on wikipedia (AM=amplitude modulation). According to some blogs and forum posts you can also have a chain of channels modulating each other, which produces very similar results to FM synth. This homebrew track uses this kind of modulation.
Interestingly, you can also make music via software synthesis made to more accurately emulate the sound of the C64 without using any samples (AHX tracker), or use the SIDmon tracker which essentially does the same thing but also allows for samples to be used (it was rarely used for games, but one example is Venom Wing). The AHX tracker was made when the Amiga gaming market had already dried up, so it was mostly used for demos. Apparently the OctaMED also features a software synth, though I'm unaware of games that use it. Two other games that use real-time synthesis (for leads and chords) are Ghost Battle and Hoi.
Many YT uploads use the PC-based Deli Player to play back songs with a joined stereo effect (giving a more centered and dynamic sound as well as making playback less muffled than on the A500), when on the Amiga the channels were hardpanned as described on Wikipedia. You could do improved software mixing on Amiga using more CPU power, though it's generally not useful in a game environment from what I understand.
Youtube Playlist (note that some tracks aren't on YT yet)
One technique that was sometimes used (for example in Toki, Battle Squadron, Hybris, Ambermoon, Bionic Commando and in tracker mods) and which gave birth to a style of Amiga music known as chipmod music to some (today it could be classified as fakebit), was to play small, single-cycle waveform samples of chiptune sounds to get C64 style waveforms, either combined with more realistic sampled drums like in other Amiga music, or sampled C64 style noise drums. This approach to Amiga music became popular in the demo scene (basically the indie scene of the period) in part because it greatly reduced the file size of each song. A trick that was eventually added to this style was to rewrite an instrument's waveform while it plays (sample offset?) to give it more character.
I don't think the C64's ring modulation and filter effects could be used for these tracks other than via sampling, but the Amiga does let you combine two channels for a 14-bit waveform, or to modulate one channel with another one as described on wikipedia (AM=amplitude modulation). According to some blogs and forum posts you can also have a chain of channels modulating each other, which produces very similar results to FM synth. This homebrew track uses this kind of modulation.
Interestingly, you can also make music via software synthesis made to more accurately emulate the sound of the C64 without using any samples (AHX tracker), or use the SIDmon tracker which essentially does the same thing but also allows for samples to be used (it was rarely used for games, but one example is Venom Wing). The AHX tracker was made when the Amiga gaming market had already dried up, so it was mostly used for demos. Apparently the OctaMED also features a software synth, though I'm unaware of games that use it. Two other games that use real-time synthesis (for leads and chords) are Ghost Battle and Hoi.
Many YT uploads use the PC-based Deli Player to play back songs with a joined stereo effect (giving a more centered and dynamic sound as well as making playback less muffled than on the A500), when on the Amiga the channels were hardpanned as described on Wikipedia. You could do improved software mixing on Amiga using more CPU power, though it's generally not useful in a game environment from what I understand.
Youtube Playlist (note that some tracks aren't on YT yet)
Body Blows Galactic (AMI), Menu
Standout tracks: Main Theme, Menu
Pinball Illusions (AMI), Intro
Standout tracks: Main Theme, Intro, BabeWatch
Body Blows (AMI)
Standout tracks: Main Theme, Russian Lab, Wrestling Arena
Turrican II (AMI)
Standout tracks: The Final Fight (Main Theme), The Desert Rocks, Traps, The Wall
Cannon Fodder (AMI), Theme
Standout tracks: Theme, Recruitment
Standout tracks: Main Theme, Menu
Pinball Illusions (AMI), Intro
Standout tracks: Main Theme, Intro, BabeWatch
Body Blows (AMI)
Standout tracks: Main Theme, Russian Lab, Wrestling Arena
Turrican II (AMI)
Standout tracks: The Final Fight (Main Theme), The Desert Rocks, Traps, The Wall
Cannon Fodder (AMI), Theme
Standout tracks: Theme, Recruitment
Fury of the Furries (AMI)
Standout tracks: Forest, Lagoon, Desert
Lotus 2 (AMI)
Standout tracks: Main Theme, Motorway Course, Credits
Pinball Fantasies (AMI)
Standout tracks: Main Theme, Billion Dollar Game Show 2-3, Speed Devils 1
Utopia (AMI)
Standout tracks: Music 3/Intro, Music 2, Music 1
Pinball Dreams (AMI)
Standout tracks: Title Theme, Beat Box Theme, Nightmare Theme
Tales from Heaven (AMI, HB)
Alien Breed (AMI)
Space Hulk (AMI)
Zool (AMI)
Assassin/Assassin: Special Edition (AMI)
Project X (AMI)
Pegasus (AMI)
Retee 2/European Champions (AMI)
Deluxe Galaga (AMI, PD/HB)
Turrican 3/Mega Turrican (AMI)
Super Cars II (AMI)
The First Samurai (AMI)
Mean Arenas (AMI)
Top Gear 2 (AMI)
Lotus III (AMI)
Captive (AMI)
Extase (AMI)
Lost Patrol (AMI)
Gods (AMI)
Alien Breed II (AMI)
Super Stardust (AMI)
Leavin' Teramis (AMI)
Dyna Blaster/Bomberman (AMI)
Unreal (AMI)
Gauntlet III (AMI), Alternate
Z-Out (AMI)
Apidya (AMI)
Slam Tilt (AMI)
SWIV (AMI)
Full Contact (AMI)
Stardust (AMI)
Shadow of the Beast (AMI)
Sensible World of Soccer (AMI)
Chaos Engine (AMI)
KGB (AMI)
Skeleton Krew (AMI)
Ghouls 'n Ghosts (AMI)
Shadow of the Beast II (AMI)
Harlequin (AMI), Theme
Jim Power (AMI)
Super Skidmarks (AMI & AMI CD32. mod)
Colonization (AMI)
Dune (AMI)
Zone Warrior (AMI)
Agony (AMI)
TFX (AMI)
Zool 2 (AMI)
Turrican (AMI)
T-Zero (AMI)
Powerglove Reloaded (AMI, HB)
Hero Quest (AMI)
Hired Guns (AMI)
Alien Breed 3D (AMI)
Fightin’ Spirit (AMI)
Chuck Rock (AMI)
Liberation: Captive II (AMI)
Jurassic Park (AMI)
Bubba 'n' Stix (AMI)
Virocop (AMI)
L.E.D. Storm/LED Storm (AMI)
Laser Squad (AMI)
Killing Game Show/Fatal Rewind (AMI)
Roadkill (AMI)
Apprentice (AMI)
Ruff 'N' Tumble (AMI)
Chuck Rock 2 (AMI)
Hybris (AMI)
Battle Squadron (AMI)
Face-Off (AMI)
Lost Vikings (AMI)
Brian The Lion (AMI)
Yo! Joe (AMI)
Lethal Weapon (AMI)
Ultima VI (AMI)
Shadow of the Beast III (AMI)
Lords Of Chaos (AMI)
Sly Spy (AMI)
Crystal Hammer (AMI)
Yogi's Great Escape (AMI)
Wolfchild (AMI)
Cedric and the Lost Sceptre (AMI)
Sabre Team (AMI)
Rogue Trooper (AMI)
Troddlers (AMI)
Amberstar (AMI)
Watchtower (AMI)
Battle Isle (AMI)
Toki (AMI)
Last Ninja Remix (AMI)
Pit-Fighter (AMI)
Torvak The Warrior (AMI), One Step Beyond (AMI), Perihelion (AMI), The Adventures of Quik & Silva (AMI), Cytron (AMI), Gem'X (AMI), Ambermoon (AMI), Magic Pockets (AMI), Elfmania (AMI), Mr. Nutz (AMI), Whale's Voyage II (AMI),
Supremacy (AMI), Fascination (AMI), Ork (AMI), Desert Strike (AMI), Venom Wing (AMI, SIDmon), Lotus (AMI), The Spy Who Loved Me (AMI), Flashback (AMI), Battletoads (AMI), The Settlers (AMI),
Breathless (AMI), Onslaught (AMI), Xenon 2: MB (AMI), Snow Bros (AMI, unreleased), Leander/Galahad (AMI), Rock 'n Roll (AMI), Skidmarks (AMI), Risky Woods (AMI), Ultima V (AMI),
Projectyle (AMI), Kajko i Koskosz (AMI), Dogs of War (AMI), Double Dragon 3 (AMI), Fire and Ice: TDAoCC (AMI), Wonderdog/Wonder Dog (AMI), Jaguar XJ220 (AMI), Shadow Fighter (AMI), Bubble Bobble (AMI), Castle Master (AMI),
Airborne Ranger (AMI), Dragonflight (AMI), Ghost Battle (AMI), Microcosm (AMI CD32 .mod)(some vocal elements) - one unused CD track, Sleepwalker (AMI), Benefactor (AMI), Alien Target (AMI), Superfrog (AMI), Premiere (AMI), Final Fight (AMI),
Best of the rest
Check: Pirates! Gold AGA, Simon the sorcerer 2 - no music?, Genetic Species - cd only?, Hexen (AMI, homebrew) 1999, Hexen (AMI, homebrew) 1999, Doom II (AMI, homebrew),
Homebrew/Demoscene tracks:
Paul Van Der Valk - Implosion 4
Jogeir - Guitar Slinger
Jogeir Collection
Best Of 1988
Captain - Space Debris & Beyond Music
Jazzcat/Appendix - Electric City
Jester - Elysium
Firefox & Tip - Hyberbased
Jungle/D&B compilation
Paradox Cracktros
Anthrox Cracktros (013, 022)
Fairlight demos
Skid Row Cracktro
Libi in Paradize - Movem
Biketommy - Ambient
CRYP77 - Fountain Of Sighs
Carter/Outbreak - Dead Feelings
Firefox - v42 etc.
Hoodlum Cracktro
Prestige Cracktro
TRSI Cracktro
Zenith Cracktro
Art of Noise - Paranoimia
Various AHX tracks (playlist)
Standout tracks: Forest, Lagoon, Desert
Lotus 2 (AMI)
Standout tracks: Main Theme, Motorway Course, Credits
Pinball Fantasies (AMI)
Standout tracks: Main Theme, Billion Dollar Game Show 2-3, Speed Devils 1
Utopia (AMI)
Standout tracks: Music 3/Intro, Music 2, Music 1
Pinball Dreams (AMI)
Standout tracks: Title Theme, Beat Box Theme, Nightmare Theme
Tales from Heaven (AMI, HB)
Alien Breed (AMI)
Space Hulk (AMI)
Zool (AMI)
Assassin/Assassin: Special Edition (AMI)
Project X (AMI)
Pegasus (AMI)
Retee 2/European Champions (AMI)
Deluxe Galaga (AMI, PD/HB)
Turrican 3/Mega Turrican (AMI)
Super Cars II (AMI)
The First Samurai (AMI)
Mean Arenas (AMI)
Top Gear 2 (AMI)
Lotus III (AMI)
Captive (AMI)
Extase (AMI)
Lost Patrol (AMI)
Gods (AMI)
Alien Breed II (AMI)
Super Stardust (AMI)
Leavin' Teramis (AMI)
Dyna Blaster/Bomberman (AMI)
Unreal (AMI)
Gauntlet III (AMI), Alternate
Z-Out (AMI)
Apidya (AMI)
Slam Tilt (AMI)
SWIV (AMI)
Full Contact (AMI)
Stardust (AMI)
Shadow of the Beast (AMI)
Sensible World of Soccer (AMI)
Chaos Engine (AMI)
KGB (AMI)
Skeleton Krew (AMI)
Ghouls 'n Ghosts (AMI)
Shadow of the Beast II (AMI)
Harlequin (AMI), Theme
Jim Power (AMI)
Super Skidmarks (AMI & AMI CD32. mod)
Colonization (AMI)
Dune (AMI)
Zone Warrior (AMI)
Agony (AMI)
TFX (AMI)
Zool 2 (AMI)
Turrican (AMI)
T-Zero (AMI)
Powerglove Reloaded (AMI, HB)
Hero Quest (AMI)
Hired Guns (AMI)
Alien Breed 3D (AMI)
Fightin’ Spirit (AMI)
Chuck Rock (AMI)
Liberation: Captive II (AMI)
Jurassic Park (AMI)
Bubba 'n' Stix (AMI)
Virocop (AMI)
L.E.D. Storm/LED Storm (AMI)
Laser Squad (AMI)
Killing Game Show/Fatal Rewind (AMI)
Roadkill (AMI)
Apprentice (AMI)
Ruff 'N' Tumble (AMI)
Chuck Rock 2 (AMI)
Hybris (AMI)
Battle Squadron (AMI)
Face-Off (AMI)
Lost Vikings (AMI)
Brian The Lion (AMI)
Yo! Joe (AMI)
Lethal Weapon (AMI)
Ultima VI (AMI)
Shadow of the Beast III (AMI)
Lords Of Chaos (AMI)
Sly Spy (AMI)
Crystal Hammer (AMI)
Yogi's Great Escape (AMI)
Wolfchild (AMI)
Cedric and the Lost Sceptre (AMI)
Sabre Team (AMI)
Rogue Trooper (AMI)
Troddlers (AMI)
Amberstar (AMI)
Watchtower (AMI)
Battle Isle (AMI)
Toki (AMI)
Last Ninja Remix (AMI)
Pit-Fighter (AMI)
Torvak The Warrior (AMI), One Step Beyond (AMI), Perihelion (AMI), The Adventures of Quik & Silva (AMI), Cytron (AMI), Gem'X (AMI), Ambermoon (AMI), Magic Pockets (AMI), Elfmania (AMI), Mr. Nutz (AMI), Whale's Voyage II (AMI),
Supremacy (AMI), Fascination (AMI), Ork (AMI), Desert Strike (AMI), Venom Wing (AMI, SIDmon), Lotus (AMI), The Spy Who Loved Me (AMI), Flashback (AMI), Battletoads (AMI), The Settlers (AMI),
Breathless (AMI), Onslaught (AMI), Xenon 2: MB (AMI), Snow Bros (AMI, unreleased), Leander/Galahad (AMI), Rock 'n Roll (AMI), Skidmarks (AMI), Risky Woods (AMI), Ultima V (AMI),
Projectyle (AMI), Kajko i Koskosz (AMI), Dogs of War (AMI), Double Dragon 3 (AMI), Fire and Ice: TDAoCC (AMI), Wonderdog/Wonder Dog (AMI), Jaguar XJ220 (AMI), Shadow Fighter (AMI), Bubble Bobble (AMI), Castle Master (AMI),
Airborne Ranger (AMI), Dragonflight (AMI), Ghost Battle (AMI), Microcosm (AMI CD32 .mod)(some vocal elements) - one unused CD track, Sleepwalker (AMI), Benefactor (AMI), Alien Target (AMI), Superfrog (AMI), Premiere (AMI), Final Fight (AMI),
Best of the rest
Check: Pirates! Gold AGA, Simon the sorcerer 2 - no music?, Genetic Species - cd only?, Hexen (AMI, homebrew) 1999, Hexen (AMI, homebrew) 1999, Doom II (AMI, homebrew),
Homebrew/Demoscene tracks:
Paul Van Der Valk - Implosion 4
Jogeir - Guitar Slinger
Jogeir Collection
Best Of 1988
Captain - Space Debris & Beyond Music
Jazzcat/Appendix - Electric City
Jester - Elysium
Firefox & Tip - Hyberbased
Jungle/D&B compilation
Paradox Cracktros
Anthrox Cracktros (013, 022)
Fairlight demos
Skid Row Cracktro
Libi in Paradize - Movem
Biketommy - Ambient
CRYP77 - Fountain Of Sighs
Carter/Outbreak - Dead Feelings
Firefox - v42 etc.
Hoodlum Cracktro
Prestige Cracktro
TRSI Cracktro
Zenith Cracktro
Art of Noise - Paranoimia
Various AHX tracks (playlist)