This is the short question but contain a lot and long answer:

NES
Super Mario Bros Series
Tennis
BaseBall
TMNT
Contra
Mappy
Donkey Kong

Sega Saturn
Sonic Series
Bare Knuckle Series
After Burner II
Contra
Double Dragon
Rambo
Mickey and Minnie Adventure
Mickey and Donlad Adventure

Game House/Mini Game
Be A King 2
Zuma
Sally Spa
Dinner Dash
Pizza Frenzy
Feeding Frenzy
Weeding Dash
Chuzzle Deluxe
Viking Saga II

PSX
Valkyrie Profile
FF7/8/9/ tactics
Alundra II
Harvest Moon
Metal Gear Solid
Legend Of Dragoon
Xenogears
Sim Theme Park
Theme Hospital
Yu-Gi-OH Forbidden Memories
Star Ocean II
Digimon World Series
Digimon Digital Card Battle
Castlevania Symphony of The Night
Tactics Ogre
Hoshigami
Super Shoot Soccer
Winning Eleven
F1 2000
FIFA Series
Gran Turismo
N-Gen Racing
Test Drive 4,5, Offroad
Dance Dance Revolution: Disney Rave
Breath of Fire IV
Road Rash
Destruction Derby:RAW
Spyro Series
Naruto: Shinobi no sato no Jinori Kasen (Forget my bad japanese)
Dragon Valor
Megaman X4, X5, X6
Legend Of Mana
RayCrisis
RayStorm
G-Darius
Brave Fencer Musashi
CTR
Nascar Rumble
Crash Bandiccot Series
Civilization II

GBA
Pokemon Emerald
Yggdra Union
Castelvania Aria Of Sorrow, Harmony of Despair, Circle of Moon
Megaman Zero 1 ~4
Yu-Gi-OH Duel Academy
Fire Emblem
Megaman Battle Network Series
Final Fantasy Tactics Advance
Harvest Moon: Friends of Mineral Town
Final Fantasy IV Advance
Kingdom Hearts Chain of Memories
jurrasic Park Town
Super robot Taisen, OG

NDS
Gardening Mama
Castlevania Order of Eclesia, Dawn of Sorrow, Portair of Ruin
Need for Speed undergorund 2
Love Plus
Avalon Code
Luminous Arc 1 & 2
The World Ends With You
Children Of Mana
FFTA2
Ragnarok DS
Shin Megami Tensei Devil Survivor
Harvest Moon Island of happiness

Doujin/Indie
HELLSINKER
Radio Zonde
Touhou Project
Akaschiverse
Ether Vapor
Chantelise
Recctear
Gadget Trial
Magical Battle Arena
Magical Battle Arena NEXT
Elemental Battle Academy
Symphony
Strke SUit Zero: Director's Cut
Beat Hazard
Minecraft
Kancolle Taisen
Mirai no Kimi Subete no Uta ni
Dysnomia
Grief Syndrome
aria
Heroine Carnival
ExCeed Series
Alltynex 2nd
magical Battle Festa
Crimzon Clover

Touhou DOujin Games
Gensou Rondo
Touhou Sky Arena Matsuri
Touhou Pocket Wars Series
Super Marisa World Series
Komajou Densetsu Series
Motto? Fushigi no Gensokyo
Touhou Diablo Treasure Hunter G
Eins Ring
Eosd For Busy Person
PCB For Busy Person
Super Touhou Wars Taisen Koumakyou, Youyoumu (Gensou Shoujo Taisen)
Memory of Gaia (The title too long... it contains Tenshi as Main Character)
Mystical Chain
Touhou Gensou Maroku: Devil of Decline
Touhou Labyrinth
MegaMari
Hypersonic Speed Girl

PC & HD Games
PES 2014
Castlevania Lord Of Shadow 2
Civilization V
Age Of Empires Series
Dynasty Warriors 8
The Elder Scroll V: SKyrim
GTA San Andreas
DMC 3,4
Naruto Shippuden 3 Ultimate Full Burst
Romance of Three Kingdom XI
MineCraft
Warriors Orochi
The Last Remnant
NFS Undergorund 2
NFS Most Wanted

Yeah... That's the game I love...
I just can't decide which the best,
But the best for coming from PSX...

Game with have FPS like Halo

hmmm... favourites out of the bunch...

Sonic Hedgehog 2
then probably, Danan the jungle fighter
Alex kid in miracle world
Gain Ground

Mario Kart
Mario All Stars
Zelda 3

Quake 
Starcraft
Warcraft
Diablo

DW 7
FF5
Etrian Odyssey 3
Hoshigami
Tactics Ogre: Knight of Lodis
FFT
Shiren the Wanderer(the wii entry)
Guardian Legend
Dragonview
Crystalis
SMB3
SF 3rd Strike
Marvel Vs Capcom 2
Gauntlet Dark Legacy
007 Goldeneye(N64)
Lufia 2
FF7
DW 6(the original only, the remake sucks)
DW5(the DS remake, the original version sucked pretty bad, but the remake is pretty epic)
Romance of the Three Kingdoms
Wizardry 5
Ragnarok Online
Atlantica Online
Might & Magic 3
Uncharted Waters: New Horizons
The original Golden Sun, 2 part game

Just to name a few

Pokémon Emerald & DP
Halo 2 & 4
Metal Gear Solid 1, 2, & 4
Marathon
EarthBound
Super Smash Bros. Brawl

Legend of Zelda (preferably Majoras Mask)
Phantasy Star Online
Minecraft
Terraria
Team Fortress 2
Monster Hunter 3 Ultimate

Kingdom Hearts
Sly Cooper
Spyro
Crash Bandicoot
The Last of Us
Uncharted
Minecraft
Diablo III
InFamous Second Son
South park: Stick of Truth

Baten Kaitos 'Eternal wings and the lost ocean'

Kid Icarus:Uprising or Fire Emblem:Awaking.

that's a tough one.......I was most obsessed with dark souls, not to say I was any good at it but I did finish it once and that was enough for me. fantastic game though.

Banjo-Kazooie.

Zelda/Okami/Shadow of the Colosuss/Pokemon/Harvest Moon/Zoo Tycoon

Metal Slug

Just one? Final Fantasy Crisis Core was when I played it years ago. So that one. I'll have to play it again. However, Nier deserves an honorable mention.

Dark Souls, Final Fantasy X, God of War

I have moved this thread to the Gaming Forum as it is better suited here. In future, please consider all the forums before posting in them.