This is tough as it has changed a LOT over the years. I remember back in the day FFVII was like the greatest thing EVER! Not anymore with all the awesome games now.

Right now it's probably:

1. The Last of Us (PS3/PS4)
2. Shadow of the Colossus (PS2/PS4)
3. Silent Hill 2 (PS2)
4. Uncharted 2 & 4 - can't decide
5. God of War (PS4 - I gotta wait until I finish this to know for sure but DAMN!!)
6. Metal Gear Solid 3: Snake Eater (PS3)
7. Need for Speed: Hot Pursuit (PS3)
8. Tekken (3, 5 & 7)
9. Final Fantasy VII (PS1)
10. ICO (PS3)

Honourable mentions: SSX (PS3), Ridge Racer(s), FFX, FFVIII, Zelda: Ocarina of Time, Streets of Rage 1&2 (Genesis), Ninja Gaiden 1&2 (NES), Castlevania: Symphony of the Night, WipEout (all of them!), Resident Evil 2, SUper Mario Bros. 3, GTAV,

Mega Man 2
Mega Man 3
Eternal Darkness
Resident Evil 4
The Legend Of Zelda: The Wind Waker
Dark Souls 2
Fallout 3
Punch-Out!! Wii
Bloodborne
Super Mario Galaxy

Ask me on a different day and most of this could change easily but
1. The Legend of Zelda: The Wind Waker
2. Super Smash Bros. for Wii U
3. Kingdom Hearts II
4. Jet Set Radio Future
5. Halo 3
6. Xenoblade Chronicles 2
7. Super Mario Odyssey
8. Sonic 3 & Knuckles
9. Dark Cloud 2
10. Pokemon HeartGold/SoulSilver

10. Fire Emblem: Radiant Dawn

9. The Legend of Zelda: Skyward Sword

8. Xenoblade Chronicles

7. Xenoblade Chronicles 2

6. The Legend Zelda: Ocarina of Time

5. Fire Emblem: Blazing Sword (GBA)

4. Tales of Symphonia

3. The Legend of Zelda: Breath of the Wild

2. The Legend of Zelda: Wind Waker

1. Fire Emblem: Path of Radiance

The order of my list changes like a woman's heart, but I feel more or less confident in the content of this list, if not the order as well.

I'll separate my list for both multiplayer and single player. Only one game per franchise


Single Player :

MGS2
Uncharted 2
Halo 2
Half-life 2
Dark Souls
Legend of Zelda wind waker
Secret of Mana
Doom 2016 (Just recently replayed it and now appreciate it more).
Resident Evil 4
Bio Shock 1


Just noticed my favorite single player games are the 2s lol.


Multiplayer:

Gears of War 4
Counter Strike Source
Halo 5
COD BO 1
BF 4
PUBG
Forza Horizon 3
Team Fortress 2
Kill Zone 2
Titan Fall 1

1.FF7
2.Metroid Prime/FF9 (tie, I keep switching these two :/)
3.FFX
4.Link to the Past
5.Super Metroid
6.Super Mario RPG
7.Resident Evil 4
8.Half Life 2
9.MGS3
10.KH2

1- Suikoden II
2 - Chrono Trigger
3 - The Legend of Zelda: Ocarina of Time
5 - Final Fantasy VI
6 - Lunar: Silver Star Story
7 - Xenogears
8 - Super Mario Bros 3
9 - Advance Wars
10 - Mega Man 3

final fantasy x

eternal darkness

Zelda OOT

half life 2

left 4 dead 2

Zelda link to the past

chrono triger

super Mario 64

resident evil 4

halo 3

grand theft auto san andreas

Tetris or Splatoon.

I like them both, not enough to make a top 10 though. I'm not a big fan of the time limit on Majora's Mask, whereas with Breath of the Wild, I simply prefer the mentioned games I guess.