Playing Liberty Island in Deus Ex for the first time. PC master race membership confirmed.

I cannot use myself as an example because I still play Playstation 2. For that matter, I don't even have a Playstation 3 or 4, nor do I have any intentions to get one.

But modern gamers are defined by any multiplayer game ever. The only ones know by name are Battlefield and Counter Strike.

Tales of Symphonia
Pokemon
Legend of Zelda 
Sword of Mana 
Okami

And

Assassin's Creed
Bioshock Infinite
Half Life 2 

Hard Truck Apocalypse
Battlefront 2
Painkiller series
Portal 2
KOTOR 2

Castlevania, specifically Symphony of the Night. I have a long running love of exploration type adventure games and multiple endings. I was so amused when I beat a boss with an item I was supposed to use in my pocket and the ending subtly called me out on it. It's also probably the biggest influence on my 4th Realm world cannon.

Devil May Cry. Again it just fed into my now long running interest in angels, demons and magical nonsense.

World of Warcraft. Don't play it anymore but the amount of fun and the connection with community I got in it has led me to keep MMO as my favored gaming platform. I don't think my girlfriend and I would have kept together long distance without the ability to adventure side by side. I did quit WoW because my Guild broke up and the community got toxic, leading a long term shyness in my new MMOs I still love the communal format.

Metroid Series, Super Mario World, Counterstrike, Starcraft series, Fallout series, Halo 1.

Sonic Adventure 2, Super Smash Bros Melee, and Need for Speed games that are on the GameCube.

All of my fav. geners are dead...
(Or at least, deformed)

Flight sims: Dead
RTS: If you don't count MOBA, then RTS is dead.
Old schooled FPS (Arena, fast paced, no recoil): Looks like it's coming back but not really. Mostly dead.
TPS: Dead

Games with a good and compelling storyline/lore along with good character development. Sure, there are common archetypes are incorporated in all forms of media.

1st or 3rd person shooters
RPGs
Fighting games
AC games
Zombie games
end of story for me.

Hyperdimension Neptunia in a nutshell.

Civ I-III had a big influence, as Sim City, SC2K, SC3k and 4. Imho, these are among the best games ever created in their respective times, especially SC4 still looks good today and that game is 12 years old now!

Games that define me are King's Quest VI, Yoshi's Island, Kingdom Hearts, and Tomb Raider (2013). Pokemon is somewhere in between this list and the "Oh, I'll play this game, since it captured my interest somehow."

Cant say if anything "defined me as gamer" since i played a lot of stuff with friends and sometimes with myself.

I do get some nostalgic shivers when looking at some good old games.. No not that company but its good too.
Soo..?

Mainly the Ninja Gaiden series,(black, sigma 1&2) I had set out to conquer those games. That or Tekken 5.

Wouldn't say as a gamer, as I'm beggining to hate this word as of lately, but The King of Fighters series defined me as a person. As a kid that grew with not much out of real role models, and that was way too overprotected, those games help me create an identity, teaching me to talk, to act, how to dress... I still see a lot of those games on the person I am today.

5 Games that define me:

1) Legend of Dragoon (I still remember playing the demo into the ground and scrounging for cash when it released)
2) Final Fantasy (can't choose just one, but I played 7 and 8 a whole lot)
3) Pokemon Gold/Silver (my favorite gen of pokemon with my favorite legends also, still love the first 3 pokemon movies)
4) Armored Core (2-Last Raven)
5) Battlefield (not my first FPS, but the one that hits the most notes in what I like in multiplayer)

Rant: You can't relive that nostalgic moment when you first played your favorite video game. It's impossible, and a remake won't do it. Your best bet is try and find new experiences that challenge your favorites for its place. Go in with an open mind. You might like something you normally wouldn't.