Long post alert!
Gameplay: DOOM 1 & 2 (PC)
The first two DOOM games on PC have felt so good to play since they came out, and still do to this day thanks to numerous source ports, modders, or even just DOS emulation. I can play using the keyboard-only layout or with an updated WASD-and-mouse-based control scheme, and love moving around with both.
Runner-up: OG Resident Evil 4 (GC, but especially on PC with the HD pack)
Every part of OG RE4's gameplay holds up IMO, so much so that I can play the GC original or PC version with HD pack and have a great time on both. Playing the game for the first time offers tension in certain areas, but on subsequent playthroughs you'll feel like a one-man army. Once you understand all the enemy attack patterns, the subtleties of moving around, and how to efficiently use your arsenal of weapons, you'll be unstoppable.
Story: Phoenix Wright: Ace Attorney
Some people think the 3rd game (Trials and Tribulations) has the best cases and plot, but I give full credit to the original Phoenix Wright/Ace Attorney. I played the shit out of the DS version, which was the first one to receive an English localization, and which I considered the gold standard as far as decent localizations (compared to what we used to get).
The dialogue is so good in both the Japanese original and the English localization, and makes each character's personality shine. And speaking of characters, I'd even argue that Phoenix is one of the most relatable and inspiring video game protagonists ever.
Play this game any way you can, it's been ported to so many systems so many times there's just no excuse.
OST: Chrono Trigger
As amazing and significant to video game music Nobuo Uematsu is, my favorite composer is Yasunori Mitsuda, who I feel outshined Uematsu with the Chrono Trigger soundtrack. The man was so dedicated to the soundtrack that he shat blood and had to have Uematsu fill in for some tracks.
I can listen to every track in the game back-to-back, or any given track on loop for an hour at a time. Brink of Time and Corridors of Time specifically might be my favorite two songs in all of gaming.
For any other Mitsuda fans, you'll notice that this soundtrack comes before he started heavily incorporating his signature Celtic style into his music (such as in Xenogears or Chrono Cross). I like both styles.
Runner-ups: Final Fantasy VII, Chrono Cross, Tekken 2
Final Fantasy VII's soundtrack left one of the biggest impressions on me when I was young. I feel all of the tracks hold up to this day, and with any track that plays I can instantly recall which scene(s) the track plays in.
I've only played Chrono Cross for about 10 minutes, but the soundtrack alone is my 2nd favorite of all time, that's how good it is. Forest of Cutting Shadows is my favorite track from it, but much like Trigger's soundtrack, I can listen to each track back-to-back or any given track for an hour at a time.
It has Mitsuda's Celtic style that I mentioned previously, along with the upgrade in music quality allowed by the PSX soundchip (and CD audio for certain tracks).
I'm not good at fighting games at all, but I love listening to the music from the Tekken games. In particular, the PSX arrangement of the Tekken 2 soundtrack. Namco went all out with their PSX-exclusive arrangements for the first 3 Tekken games. The fact that you can toggle between the arrangements or the originals makes these games
GOAT'd as far as fighting games.
Graphics: Resident Evil Remake (GameCube)
This is the game whose graphics wow'd me the most in my gaming life, compared to anything I had seen before. It was such an improvement on RE1's and RE2's graphics, and made the original game actually scary to me.
Runner-ups: Metal Gear Solid 2 (PS2), DOOM 2016 (PC)
MGS2 was the biggest jump in graphical improvement I've ever felt in my gaming life. It was also the game that made me say "so THIS is what the PS2 has to offer!"
DOOM 2016 blended the feel of the DOOM universe with the sensibilities of a modern FPS, and improved on them as well. Another game that made me say "holy shit this is so good."