It's a tough one so I'll put them into categories or I'll never decide...
First Person Shooters
Counter Strike: Source has to be my fave of the lot. Multiple game types, most for fun, the original creator of the gungame mode, surf maps, low gravity sniper fights... You name it, they have it. I've put over 1000 hours into that game, been with multiple massive communities (those who know being the only competitive one) and been an admin for many a server, but those groups slowly drifted apart and with cs:go so did the rest of the community.
Story Telling
It was a close call between Last of Us and Walking Dead, but LoU takes it for me. The starting has caused many people to shed a manly tear or two, and the entire setting of the game is just phenomenal. It's a game that people say lacks replay value but I have played through the game 4 times and have not yet tired of it. If just to hear the story one more time.
Action/Adventure
No question that Legend of Zelda takes precedence here. However which one is the true question that many can never answer. I am one of those people... I have a top 5 and they are never the same whenever I go through them! Ocarina of Time, Majoras Mask, Link to the Past, Windwaker, Twilight Princess... Even the less popular gameboy games such as Minish Cap! There are too many choices that boggle my mind each time I think about it, so lets just leave it at the series in general :p
RPG
There is one series in particular that grabs my attention. However, out of the 3 games they have made so far, Mass Effect 2 is easily my choice for the best rpg I've played. The first game of the series begun the story and had the biggest rpg feel to it, however with the things it lacked, Mass Effect 2 delivered. A greater emphasis on the characters themselves and the action that was Commander Shepard, also... Tali...
There are two things that I was sad to see leave the mass effect series between 1 and 2, those being the Mako (why people hated that machine I will never know... It was the level layouts fault not the mako!) and the loot. Loot being one of the bigger things that started to make the series lose it's RPG feel and become more of a third person action shooter that I know Mass Effect 3 to be. However Mass Effect 2 still held enough of the rpg feel for me to put it ahead of it's predecessor on this list.
Strategy
There are two different types of strategy games I will put into this. Turn Based and Real Time. I have played many a strategy game be it Civilization, Tropico, Anno, Age of Empires, Europa or Crusader Kings, there are many with varying depths of difficulty and complexity. Crusader Kings I would call a RTS game, and one I have played only a small amount compared to a lot of my other games, but one with such a high level of complexity that it draws my attention completely.
The idea of starting a game where you are just a simple merchant, and working the feudal system in such a way that you enable yourself to marry into a position that one day will make you king... Or perhaps you wish to start AS the king/queen him/herself, and work on taking control of a specific area, perhaps even the world... Lest you go on a hunt and get mortally wounded by a fluffing boar!
As for turn based strategy I would say that civilization has taken my fancy as of late. I do not own the latest of the series but from what I've seen they have only improved of civ 5, adding newer tactical options for dominating your opponent in the form of the Miasma and local alien wildlife. I am always a sucker for the complex games such as those, but should a more simple tbs game wish to take the top spot, XCOM is extremely close behind!
Even with all these categories I have such a hard time deciding lol
First Person Shooter - for me would be Call of Duty UO or Call of Duty 2. (never really played the others CoDs after that).
MMO - Well World of Warcraft mainly cause of the sheer hours and memories i have from that game but Age of Conan PvP really caught my attention for a while untill my friends left the game cause their PCs were to crap.
RPG - Though one. Has to either be Mass Effect trilogy or Dragon Age Origins. Maybe Inquisition will be added to that list? (The Walking Dead, The Last of Us and The Wolf Among us are close contenders to)
Strategy - This one would be the hardest for me to pick as strategy is my favourite type of game. I've played Crusader Kings II , Age of Empires (all of them), Age of Wonders (all of them), All Total War games (i'm a massive Total War fan), Civilization (ofcourse!), Divine Divinity Dragon Commander was really fun. Unique kind of game, The Stronghold series, Spellforce (all games +dlcs). Probably forgot a few (Red Alert and C&C) but these are my most fun strategy games.
Action / Adventure - The Darksiders series and Dust: an Elysian Tail was an amazing game.
There are just to many good games to just mention one so here was my list
Especially when it's about the games I love... There are some I can go on forever about! I might even be putting Mass Effect 3 in that list soon, I'm playing through the series again with all the DLC and an added "happy ending" mod for ME3 that doesn't have all the rubbish plot hole creating cutscenes of laziness that was (in my opinion) the bad ending of a great series. Who knows though, I expect it will make the game much more enjoyable at least, but not good enough that it could top any of my current list
Of all time? Theres so many recent games people have mentioned, but of all time, I'd have to say Baldur's Gate 2, Everquest, Ogre Battle 64, FTL and honestly I'd be lying to myself if I didnt say League of Legends. My gameplay of all these games is in the 100s of hours, 1000s of hours for EQ and LoL.
Me and Cohh have similar tastes. Either Skyrim or Deus Ex: Human Revolution. They both have an amazing soundtrack, Deus Ex has the story but Skyrim has the general gameplay and replay value. Tough decision to make but they are both incredible games.
This is really hard and probably not my real list, only ones i can remember..
MMO - during it's time, it has to be Lineage2, great art, soundtrack, community and castle/fortress siege pvp. Closely followed by Phantasy Star Online and Final Fantasy XIV - Realm Reborn. I really hope Black Desert and Lost Ark can bring in a new era, Archeage was just disappointing.
FPS - hard one... Battlefield 2/ Project Reality took alot of hours out of my life and had loads of fun. Counter Strike Source as someone mentioned, theres tons in there. Borderlands 2 is great too (only with friends tho). Insurgency co-op is something i play alot atm.
RPG - I havent really played many tbh.. Final Fantasy series.. oh and Golden Sun back in GBA days
Strategy - Final Fantasy Tactics and right now Divinity Original Sin... loved Fire Emblem series Advanced Wars too.
Driving - Eurotruck Simulator 2 (lol yeh i dont play much driving).. Mario Kart series.. The Crew was bitterly disappointing.
Story Action - hands down Metal Gear Solid series, my fav ... bring on Phantom Pain nowwwwwww.... Shadow of Colossus was unique and fun to me too
MMO - World of Warcraft hands down. I've met so many amazing people from WoW. It has a number of casual or hardcore ranging elements within the same gametype (pet battles while leveling or the tourneys, PVP for fun or for arena glory, garrison missions for a time waster or for min-maxing your characters, PVE from scenarios to dungeons to raids in LFG or guilded Mythic mode, quests to just level or earn Loremaster, etc.)
FPS - The Halo series is great in gameplay as well as art and story. Simply amazing and the number 1 reason to have any Xbox console.
RPG - Star Wars: Knights of the Old Republic. A gorgeous game in play and art that held true to the feel of Star Wars lore but still could have stood alone if you removed the IP.
Story - The Walking Dead. Clementine, Lee, Kenny... such great characters. Can't wait for season 3!
Fighting - Super Smash Bros. Many childhood friendships ruined and forged!
Strategy - This War of Mine. It's fun to play from the perspective of civilians on their last stand.
I don't really have a 'favorite', really. There's no way for me to ever choose a favorite.
Super Mario Bros and Mario 3 and Super Mario World... early Mega Man titles... Sonic 1-3. I play through the entire games at least once a year. The older console systems will forever hold a special space in my heart.
Counter-Strike 1.6. I've come back to that game over and over and over and over since it began, just about. I don't think I'll ever tire of it. 24/7 Dust, bay-bee.
....aaaand World of Warcraft. My ultimate guilty pleasure. I'll be there 'til it dies.