I've played countless games over the years, and sometimes I have a hard time determining what my favorite game actually is. Some games have left a deep impression upon me, and others are just simply fun to play. Trying to actually rank these games is really an impossible task, to be honest. Instead I'd rather just provide a blurb about why each game is special to me.
The Legend of Zelda
The original 8-bit Zelda adventure cannot be omitted from this list. This game occupied many hours of my time in grade school and set the stage for my lifelong love of fantasy adventure games and RPGs. It also spawned one of the greatest game series of all times. While Zelda feels a bit clunky now, it is still a fun game to play every once in a while for nostalgia's sake in order to go back to the roots of the series.
Final Fantasy IV
The original 16-bit Final Fantasy title practically defines the JRPG subgenre. In a large departure from the 8-bit games I had played previously, where the story was generally relegated to the manual, FFIV actually had a cohesive in-game narrative and characters with personalities. Though often regarded as cheesy by today's standards, this game's story captured my imagination in ways that previous games had not. When in a pinch I often site FFIV as my favorite of all time simply because of the lasting impression it made upon me. This game has been remade a number of times, and I can surprisingly recommend the DS version since it did a pretty good job of translating everything into 3D without wrecking the game.
The Legend of Zelda: A Link to the Past
The 16-bit Zelda offered a bigger and better adventure than the original in just about every way possible. Not only were the graphics and sound more advanced, but the world and story were expanded upon. Link's arsenal was also improved with items like the Hookshot. As with many of Nintendo's first party 16-bit titles, this game stands the test of time very well and is still better than the majority of games released today. It also solidified much of the lore behind the world of Hyrule and set the stage for the subsequent games in the series.
The third title in the Metroid series was a winner and solidified what it meant to be a Metroidvania game before the term was even coined. Much like 16-bit Zelda, it offered a bigger and better game than the 8-bit original by expanding the game map and giving Samus a bunch of cool power ups. The game also provided a great ambient atmosphere (by 16-bit standards) by making use of the console's sound capabilities. Super Metroid also remains a favorite for speed runners.
Final Fantasy VI
While I personally prefer FFIV just a bit more, FFVI is a close runner up in my book (and many gamers do prefer it). It features a bigger cast of characters and is an overall longer game, though I personally feel that it is a bit too easy. It is one of the most impressive 16-bit classics from a technical perspective, featuring excellent sprite art and a memorable soundtrack.
In the same vein as the 16-bit FF titles, Chrono Trigger is also a classic and is technically even more impressive than FFVI, with yet another awesome soundtrack and some of the most impressive sprite work of the era. Towards the end of the 16-bit days, Square's titles pushed the limits of the hardware in many ways. Frankly many of these games (in retrospective) look better than the early PS1 games that followed.
Castlevania: Symphony of the Night
The original Metroidvania-style Castlevania game. It featured excellent game play and a huge map with many hidden secrets, large bosses, and a rocking soundtrack. This is a game I replayed quite a bit on my PS1, and it may even edge out Super Metroid as my favorite Metroidvania game.
The Legend of Zelda: Ocarina of Time
The original 3D Zelda game, and (in my opinion) the best N64 title. Ocarina of Time is an epic adventure and paved the way for many 3D adventure games that came after it. It built upon the lore established in A Link to the Past and improved the story aspects of the series even more. Nintendo also managed to do a great job fixing the camera issues that plagued earlier 3D games (including Super Mario 64 by introducing an innovative targeting system. The 3DS version that came out later improves the game's models and textures (it also includes the Master Quest), so I recommend picking that version up if you've never played it.
Street Fighter III: Third Strike
My personal favorite fighting game, though I readily admit I suck pretty badly at it. There isn't much to say here. I just really like a lot of the characters as well as many of the mechanics it introduced, including parrying. It is also the game that elevated Daigo into legendary status. The spritework in this title is very impressive as well, and it is a shame that we didn't see many other games on the CPS3 hardware before Capcom abandoned it in favor of 3D-based engines.
Lunar 2: Eternal Blue Complete
A remake of the 16-bit Sega CD title, Lunar 2 is a classic anime-style 2D JRPG with a compelling story and characters. It also had a higher difficulty curve than the 32-bit Final Fantasy games. While Lunar: Silver Star Story got remade again for the GBA and then PSP, Eternal Blue has not seen any such love since the 32-bit era. Sad, because I feel the sequel is a stronger game. It is also a shame that the series has not really gotten much love in recent years at all. Personally, I'd love to see someone make a new Lunar game with Tales-style combat. I honestly think that would work out really well, but maybe that's just me. The English-language version of this game is notorious for the crazy pack-ins as well, which I can proudly say I still have preserved in the original game box.
Final Fantasy IX
Personally, I felt that Final Fantasy VII is the most overrated game of all time, and that Final Fantasy VIII is just plain garbage. I almost passed on FFIX entirely, but am glad I didn't. To me, FFIX ended up being a nice callback to the 16-bit titles I was more fond of. Like almost every 32-bit game Square made, the story does get oddly weird and disjointed at the end, though it gets bonus points for Vivi to make up for it.
Quake III Arena
My personal favorite FPS of all time. This is also one of the few games I was actually relatively good at on a competitive level, though not exactly professional grade, but I spent many hours fragging away from my dorm room. I am very much looking forward to the upcoming Quake Champions, even though I know I no longer have the reflexes of a 20-year old and will likely get pwned while trying to rocket jump again.
Another game I spent way too much time playing back in the day. Overall I preferred Diablo II over Diablo III for a variety of reasons, though I cannot deny the possibility nostalgia played a big factor. I always used to love playing through the game while trying out different types of build, and I have a soft spot for Deckard Cain. There isn't much to be said except that this is a classic clicky action RPG.
I personally consider Metroid Prime to be the best first party title on the Game Cube, even better than Wind Waker. When it was announced I was skeptical about it, but I ended up loving the way they transitioned the series into 3D without screwing it up. It is unfortunate that Nintendo had to destroy the series with Other M. This game is far superior, and takes a lot of queues from Super Metroid when it comes to setting up a game with excellent atmosphere and exploration.
NWN was more than just a game. It was an ambitious title that implemented 3rd. Edition Dungeons and Dragons relatively well on the PC. While the main game was merely OK compared to Baldur's Gate, the real reason NWN was great was because it included a very powerful game editing tool and a vibrant mod community. The community created many impressive modules that you could play online with your friends. The Hordes of the Underdark expansion was also quite impressive when stacked up against the original quest.
Tales of Symphonia
ToS is the first Tales game I played and I was instantly hooked to the story and combat. It executed many JRPG cliches well and provided a huge amount of replay value, and a cast of enjoyable characters. Even though this game has clunky combat compared to later games in the series, it is still a great title to play through. The dungeon design and puzzles are also very good, which is something later games have had issues with. While the original Game Cube version is hard to come by, there was a PS3 re-release that also includes the Japanese voice track, though this is one of the few games that the English voices are actually good.
World of Warcraft (Vanilla & TBC)
Unfortunately, I spent so much time in this game that I couldn't justify leaving it off. WoW was the game that popularized the MMORPG to the unwashed massees. Unfortunately, it also partially ruined the genre. To this day, the majority of MMORPGS, even the good ones, are WoW clones.
I also think that the game lost its soul with Wrath of the Lich King. The original game and TBC kept a good balance of challenge, time sinks, exploration, and the need for maintaining a community of other players. At the same time, it wasn't as needlessly grindy like EQ or FFXI. Blizzard maintained a tedious balance in the early days, but threw it out after the 2.x line in favor of instant gratification mechanics that made the game even more accessible, but at the cost of the game's community.
Arguably there are other MMOs that have surpassed WoW, but the glory days of raiding Blackwing Lair are hard to forget. I doubt I will ever go back to the game at this point, even though quite a few of the people I used to raid 40-mans with still play it religiously.
The Legend of Zelda: Twilight Princess
Personally, I feel that Twilight Princess perfected the OoT formula. While possibly an unpopular opinion, I like this game just a bit better than the other 3D Zelda titles. People do criticize it for being very same-ish, but I personally feel this is the first version of Hyrule on display that actually feels like a lived-in world. I also thought the slightly darker and more serious tone of the game work to its favor. Midna is my favorite helper character the series, since she has her own motivations in the story aside from just helping Link. Also, dual Hookshots.
Tales of Vesperia
While I enjoyed all of the Tales games to a degree, ToV is probably still my favorite. I think it still has the best combat in the series as well as some of the coolest characters (though ToB comes close in both areas). This is a game I liked enough to import the Japanese PS3 version, because it added even more stuff when compared to the original XBox360 version. ToV is a game I replayed quite a bit in order to complete all of the side quests and optional item collections.
The Elder Scrolls V: Skyrim
It is often a subject of disagreement when it comes to which Elder Scrolls game is actually the best. While an argument can be made for each one, practically, I personally think that the most recent entry is the best from a game play perspective. Daggerfall does not stand the test of time well, and Oblivion suffers from a certain clunkiness even though the main story quest and many of the guild quests are arguably better written. I also shamefully admit I didn't actually play Morrowind, which a lot of people prefer. Even several years later, Skyrim continues to have an active and vibrant mod community, which adds longevity to the game. I have hundreds of hours logged, but I still discover something new with each playthrough. It doesn't hurt that I'm currently running Skyrim SE with over 200 mods, which makes the game look pretty impressive on my high end hardware.