Among several games that immediately drew me in include Heavenly Sword, Dead Space, Darksiders, Bejeweled, DOOM, Mortal Kombat, Tekken, House of the Dead, Bayonetta, Virtua Fighter, Soul Calibur, and Killer Instinct.
Recently Conker’s Bad Fur Day and Ori and the Blind Forest
Fallout, Halo, Doom, Killer Instinct, Diablo 2, Carnivores,and Starcraft/Warcraft all come to mind.
World of Warcraft got me bad when it first came out. Kinda blew my mind at the time.
Halo, Spyro, Mortal Kombat, Killer Instinct, Mass Effect, Crash Badicoot, Skyrim, SSBB and Star Wars Battlefront.
Just going to go top 5:
Halo
Killer Instinct
Oblivion
Fallout 3
Spyro
Solar Striker
Super Mario Land 2: Six Golden Coins
Gargoyles Quest
Operation C
Mega Man 3
Double Dragon 2
Super Mario 3
Streets of Rage 2
Mortal Kombat
Mortal Kombat 2
Weaponlord
Eternal Champions
Primal Rage
Killer Instinct
Panzer Dragoon
Panzer Dragoon Zwei 2
Ultimate Mortal Kombat 3
Night Warriors: Darkstalkers Revenge
Virtua Fighter 2
Final Fantasy VII
Final Fantasy Tactics
NHL 98
Castlevania: Symphony of the Night
Blood Omen: Legacy of Kain
Suikoden
Tekken 3
Silent Hill
Need for Speed: High Stakes
Soviet Strike
Star Ocean: The Second Story
Crash Bandicoot
WCW/NWO Revenge
Soul Calibur
Skies of Arcadia
Resident Evil: Code Veronica
Legacy of Kain: Soul Reaver
Grandia 2
NFL 2K
World Series Baseball 2K2
NBA 2K1
Power Stone
Gauntlet Legends
Mortal Kombat: Deadly Alliance
Mortal Kombat: Shaolin Monks
Legacy of Kain: Defiance
Gran Tourismo 3 A-Spec
Dark Cloud 2
SSX
Twisted Metal Black
Devil May Cry
Ico
Virtua Fighter 4
Crimson Skies: High Road to Revenge
Aggressive Inline
MechAssault
MechAssault 2: Lone Wolf
Hunter: The Reckoning
Marvel Vs Capcom 2
Rogue Leader: Rogue Squadron 2
Gears of War
Guitar Hero 3
Blur
Lost Odyssey
Mortal Kombat 9
Need for Speed: Most Wanted
Metal Gear Solid 4
Batman: Arkham Asylum
Batman: Arkham City
New Killer Instinct
Ori and the Blind Forest
Middle Earth: Shadow of Mordor
Dragon Age: Inquisition
That’s about all I can think of. But yeah, within five minutes of putting these games in, I was hooked. I knew what I wanted to do for the next day, week, month, etc.
Not an exhaustive list, but these are the ones that REALLY got their hooks in me.
DOOM, StarCraft, and Street Fighter Alpha 3. I still play all 3 religiously (and SFA3 is online with fightcade!!!)
Killer Instinct (All of them), Mortal Kombat X, Super Mario Strikers, MGSV: The Phantom Pain, Minecraft, Street Fighter Alpha & SFA 3, and Oddworld: New N’ Tasty (MY CHILDHOOD GAME REBORN). So yeah.
Well Resident Evil drew me in long before i even saw it being played. Even longer before I played it myself.
Back in the magazine reading 90’s =P
Killer instinct 2013. Watched hours of youtube videos because I didn’t own an xb1. But I knew that as soon as I had money that I was going to buy KI.
Mass effect 2. This time I had no xb360 and didn’t know what Mass effect was. Then finally ME2 came out for ps3 and I hated myself for not paying attention to this game sooner. Shows how bad console exclusives are, lol. One of my favorites on previous gen consoles.
killer instinct, kingdom hearts, uncharted, legend of dragoon, devil may cry 3, tony hawk pro skater 5 ( game of the year 
), gears of war ultimate ( my first gears game was the best experience ever!!!), street fighter 5, monster hunter.