While there are various other outliers such as TD view Zelda-likes and ARPGs, I've focused on 2D sidescrollers (and later TP view platformers) here. See my worlds unraveled site for info on games in other perspectives.  

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1994: 

The Elder Scrolls: Arena (PC, 1994)?

Blood Gear (PCE CD, 1994)(Untranslated)?

Generations Lost (MD, 1994)

Sinaria: Lost in Space (PC, 1994)
King's Field (PS1, 1994)

Wario Land: Super Mario Land 3 (GB, 1994)

Ganbare Goemon 3 (SNES, 1994)
Blackthorne/Blackhawk (SNES etc, 1994)

Legend of Xanadu (PCE CD, 1994)
Umihara Kawase (SNES, 1994)

Mega Man V (GB, 1994)

Benefactor (AMI, 1994)

​Ecstatica (PC, 1994)

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1995: 
Phantom 2040 (SNES/MD, 1995)
Bioforge (PC, 1995)? - WIP
CyberMage: Darklight Awakening (PC, 1995)?
Kishin Douji Zenki (GG, 1995)
Hexen: Beyond Heretic (PC, 1995)
Hyper Iria (SNES, 1995)
Magical Pop'n (SNES, 1995)
​Tales of Phantasia (SNES, 1995/PS1/GBA)
Legend of Xanadu: Kaze no Densetsu Xanadu II (PCE CD, 1995)
Star Wars: Dark Forces (PC, 1995)
Bermuda Syndrome (PC, 1995)?
Beavis and Butt-head (MD)?
Donkey Kong Country 2 (SNES, 1995)
MechWarrior 2: 31st Century Combat (PC, 1995)
Star Trek: Deep Space 9 - Crossroads Of Time (MD/SNES, 1995)
Ganbare Goemon: Kirakira Douchuu/Ganbare Goemon 4 (SNES, 1995)
Asterix and the Power of the Gods (MD, 1995)

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1996: 

Vigilance on Talos V (PC, 1996)
DoReMi Fantasy (SNES, 1996)
The Elder Scrolls II: Daggerfall (PC, 1996/2015 (Unity ver.))
Strife (PC, 1996)
Super Mario 64 (N64, 1996/NDS, 2004)
OverBlood (PS1, 1996)?
​​Realms of the Haunting (PC, 1996)?
Terra Nova: Strike Force Centauri (PC, 1996)
Tail of the Sun (PS1, 1996)?
Deus (PC, 1996) 
Azrael's Tear (PC, 1996)
Tomb Raider 1-3 (PS1, 1996)

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1997: 

Last Imperial Prince (PC-FX, 1997)? - WIP
Star Trek: Generations (PC, 1997)? - WIP
Dark Earth (PC, 1997)? - WIP
Dr. Franken II (GB, 1997)
Sorcerian Forever (PC, 1997)
Lego Island (PC, 1997)
Pax Corpus (PC/PS1, 1997)?
Men in Black: The Game (PC, 1997/PS1, 1998)?
Goosebumps: Attack of the Mutant (PC, 1997)?
​Star Wars: Jedi Knight: Dark Forces II (PC, 1997)
​​​Turok: Dinosaur Hunter (N64/PC, 1997)
Hexen II (PC, 1997)?
Princess Crown (SAT, 1997/PSP, 2005)
Quake II (PC, 1997/Multi)
​Oddworld: Abe's Odyssey (PS1/PC, 1997)
Umihara Kawase Shun (PS1, 1997)
​Nightmare Creatures (PC/PS1, 1997)?
Tales of Destiny (PS1, 1997)
Bomberman 64 (N64, 1997)
Armored Core (PS1, 1997)
Crash Bandicoot 2 (PS1, 1997)
Nanatsu Kaze no Shima Monogatari (SAT, 1997)?

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1998: 

Medievil (PS1, 1998)

Sonic Adventure (DC/GC, etc., 1998)

Half-Life (PC, 1998)
​Wario Land 2/Wario Land II (GB/GBC, 1998)

Unreal (PC, 1998)
​Spyro the Dragon (PS1, 1998)

Montezuma's Return (GB/GBC, 1998) 

Tail Concerto (PS1, 1998) 

Body Harvest (N64, 1998)

Metal Gear Solid (PS1, 1998)

Tenchu: Stealth Assassins (PS1, 1998)?

Overblood 2 (PS1, 1998) 

Trespasser (PC, 1998)?
Heretic II (PC, 1998)? 
Die by the Sword (PC, 1998) 
Quest for Glory V (PC, 1998)?
Thief: The Dark Project (PC, 1998) 
Oddworld: Abe's Exoddus (PS1/PC, 1998) 
Delta Force (PC, 1998)? 
Soukaigi (PS1, 1998)? 
Akuji the Heartless (PS1, 1998)? 
Queen: The Eye (PC, 1998)
Ganbare Goemon: Kurunara Koi! Ayashige Ikka no Kuroi Kage (PS1, 1998)? 
Jumpy's World (PC, 1998)?
Dolphin's Dream/Diver's Dream (PS1, 1998)? 
Bomberman Hero (N64, 1998)? 
Turok 2: Seeds of Evil (N64, 1998)?
Asghan: The Dragon Slayer (PC, 1998) 
Montezuma's Return (PC, 1998, 1998) 
Return to Krondor (PC, 1998)? 

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1999: 

Ape Escape (PS1, 1999)

Sorcerian Original (PC, 1999)?

Tomb Raider: The Last Revelation (PC/DC, 1999)?

Valkyrie Profile (PS1, 1999)?

Rayman 2 (N64/PC, 1999/PS1/DC, 2000)

Hype: The Time Quest (PC, 1999)?

Urban Chaos (PC, 1999/DC/PS1, 2000)

Indiana Jones and the Infernal Machine (PC, 1999/N64, 2000)?

Rittai Ninja Katsugeki Tenchu: Shinobi Gaisen (PS1, 1999)?

Omikron: The Nomad Soul (PC, 1999)?

King's Quest: Mask of Eternity (PC, 1999)? - 1998?

Star Wars: Episode I: The Phantom Menace (PC/PS1)?

Spriggan: Lunar Verse (PS1)?

Maken X (DC, 1999)?

Rising Zan: The Samurai Gunman (PS1, 1999)?

Soul of the Samurai (PS1, 1999)?

Xena: Warrior Princess (PS1, 1999)?

Nocturne (PC, 1999)?

​Septentrion: Out of the Blue (PS1, 1999)?

Vampire Hunter D (PS1, 1999)?

Dragon Valor (PS1, 1999)?

Lands of Lore III (PC, 1999)?

Crusaders of Might and Magic (PC, 1999)
​Silver (PC, 1999)
​Shenmue (DC, 1999) 
Drakan: Order of the Flame (PC, 1999) 
​Everquest (PC, 1999)
Hybrid Heaven (N64, 1999) 
Soul Calibur/SoulCalibur (DC, 1999)(Mission Mode)?
Spellbinder: The Nexus Conflict (PC, 1999)? 
Bomberman 64: The Second Attack! (N64)? 

​

2000: 

​Mega Man Legends 2 (PS1, 2000/PC, 2003/PSP, 2005)

Deus Ex (PC, 2000) - 3D ARPG/Stealth/FPS Hybrid
Spyro: Year of the Dragon/Spyro 3 (PS1, 2000)

Bionic Commando: Elite Forces (GBC, 2000)?

Spider-Man (GBC, 2000)
Armored Core 2 (PS2, 2000)?
Paper Mario (N64, 2000)?
Daikatana (GBC, 2000)

Nox (PC, 2000)
Dark Cloud (PS2, 2000)?
Tenchu 2: Birth of the Stealth Assassins (PS1, 2000)?
"Tales of Destiny II"/Tales of Eternia (PS1, 2000)
Spider-Man (PS1/PC, 2000)
Napple Tale: Arsia in Daydream (DC, 2000)(Untranslated)?

​

2001:

Legend of Zelda: Oracle of Seasons (GBC, 2001)
Technomage: Return of Eternity (PC/PS1, 2001)?
​Ico (PS2, 2001/PS3, 2011)
Jak and Daxter: The Precursor Legacy (PS2, 2001)
Baldur's Gate: Dark Alliance (PS2, 2001/GC/XB, 2002/GBA?, 2004)?
Grand Theft Auto III (PS2, 2001/PC, 2002/XB, 2003)?
Severance: Blade of Darkness (PC, 2001)
Project Eden (PC/PS2, 2001)
Extermination (PS2, 2001)
Wario Land 4 (GBA, 2001)

Level-based and linear: 
Conker's Bad Fur Day (N64, 2001)
Devil May Cry (PS2, 2001) Hack 'n Slash w/ AA elements 
Illbleed (DC, 2001) - 3D Action/Survival Horror
Batman: Vengeance (Multi, 2001/PC, 2002) - TPS/Action Platformer
Spider-Man 2: Enter: Electro (PS1, 2001) 
​Oddworld: Munch's Oddysee (XB, 2001/Multi, 2010 (Remaster)) - Puzzle Platformer w/ RTT elements