A "favourite game" to me is generally a game in which I am immersed or engrossed in it from beginning to end. I place importance on two main factors: story and music. A good story consists of one or all of the following: 1) Memorable and reasonably developed characters in which you care about their trials and tribulations; 2) The course of events inspires positive (e.g. happiness) or negative emotions (e.g. sadness) and/or encourages you to think on a deep(er) level; and 3) Plot twists. Note that my favourite games skew more towards retro games and hence may be "tainted" by nostalgia/rose-coloured glasses. Possible spoilers.
NINTENDO FAMICOM (NES)
Rockman 3: Dr. Wily no Saigo! - My favourite out of the six Nintendo Rockman games, as well as being my favourite Rockman soundtrack for this console. Also, I like this game's sound effects better than the prequel.
Memorable moments:
The return of the Rockman 2 bosses and the "destroyed/corrupted" versions of the four original stages.
NINTENDO SUPER FAMICOM (SNES)
Akumajou Dracula (Super Castlevania IV) - I bought this game before I even got the console to play it on. This game seems pretty much perfect. Excellent graphics, varied and unique stages, atmospheric, and of course, the music. Gameplay-wise, the new whip-handling and changing directing while jumping are welcome additions.
Memorable moments:
The dark atmospheric intro.
The quiet and short opening stage (crossing the drawbridge) culminating into the raising of metal gates and the blasting of "Simon's Theme".
I particularly like the gold/treasure chest stage and stage music.
The consecutive battles with Dracula's minions/Death along with the continuous ominous music.
The playing of "Simon's Theme" again when Dracula is near-death.
Breath of Fire II: Shimei no Ko - In hindsight with my now more critical mind, the story does take a while to get going and contains a few too many fetch quest detours, but once the story does get started, it is very engrossing, very tragic, and takes many twists and turns. The battle scenes are a highlight, with full-size sprites and detailed animation (a nice change from e.g. Final Fantasy's small battle sprites and limited animation). And like the prequel, the party consists of multi-race/species companions. Lowlights include the very high encounter rate and overuse of some music (standard dungeon theme), or slightly painful to my ears music (standard town theme). Also, unfortunately, some or most of the party members are irrelevant to the core story.
Memorable moments:
The intro, beginning with Ryuu taking a nap and waking up to find that all the villagers have become strangers, the unbeatable Demon boss battle, and the epic conclusion to the intro: the synchronisation of the "Breath of Fire II title theme" and the "shutting" of the wooden Breath of Fire II logo door.
The frog castle saga.
The monkey fortress saga (and epic battle between Sten and his rival on falling rock platforms).
The dream world and the world map music.
Nina's sister's sacrifice.
The entire religious city infiltration section with the loss of non-player character lives, the death of the good bad guy, the solely organ music, and the reunion of Ryuu and his father.
The first-half of the final dungeon with its trippy LSD-inspired background.
The re-encounter with the demon from the beginning of the game.
The realisation that this demon doesn't really care about his boss' goals, he just wants a fair one-on-one fight with a worthy opponent i.e. Ryuu (See Gouki from Street Fighter, also a Capcom game).
The entire pre-final boss sequence with the killing of Ryuu's party members and Ryuu running "Through the Fire and Flames" in a fit of rage.
Other neat stuff: overworld music changes (twice), mid-game battle music change (once).
Chrono Trigger - Like BoF1, this was never released in PAL territories so I couldn't get any nostalgic benefit from it (played the game years later via emulation). So I can't quite wax lyrical as much about it like I did BoF2. Also struggling to think of memorable moments because they aren't etched in my brain. Suffice to say that I have no complaints about this game.
Estpolis Denki II (Lufia 2) - Probably the most addictive RPG I've played and replayed, which makes sense since this is a very puzzle-oriented game. Good music (particularly the battle themes), surprisingly detailed battle system (IP moves, capsule monsters, etc), nice and large enemy sprites, and a sense of satisfaction every time a puzzle room is solved. And then there's the Ancient Cave, the rouge-like dungeon which is arguably more addictive than the main game. Weak points include a relatively uninteresting story filled with fetch quests and samey-town and samey-dungeon designs. The fact that enemies can be avoided (a rarity in RPGs those days) is a definite plus.
Memorable moments:
After some big events, some downtime and plot progression with the marriage between Maxim and Selena.
Getting the submarine and exploring underwater (I have a particular fascination with underwater bits in games).
The biggest mountain dungeon (one of the last dungeons), the one where you fight a dragon boss. Noteworthy due to the scale and size of it and knowing the game will finish soon.
Ancient cave memorable moments: basically trying to survive! Also, encountering unique name pallete-swapped monsters or completely unique monsters (e.g. Lucifer, the big 3 metal dragons etc), reaching the last level for the first time and encountering the giant zoomed-up slime.
Final Fantasy USA: Mystic Quest - I don't know why I like it, but I just do. Perhaps I had an RPG drought at the time (not impossible given PAL) and this game hit the spot. Ryuji Sasai's heavy rock music score definitely helps. The enemies showing signs of damage is also a nice gimmick.
Memorable moments:
The screen wraparound volcano/lava dungeon.
Pazuzu's Tower: I like towers, the music used here, and the fact that you know the end of the game is coming.
Final Dungeon: Awesome dungeon theme, and multi-level locations with differing scenery (ice stage, lava stage etc).
Final Fantasy VI - In all honesty, I never saw what the big deal was with the ATB battle systems. I'm here for the story and FF6 delivers.
Memorable moments:
The staff credit intro with the armours walking up the snow, to the tune of "Tina's Theme".
Phantom Forest and Phantom Train sections give a sense of mystery and wonder.
I never expected to see an Opera House and opera performance in a video game.
The multi-stage final battle with lots of organ instrument use.
Gaia Gensouki (Illusion of Gaia) - Souls don't exist (unless science proves it does), but if souls did exist, then they would reside in Gaia Gensouki and Tenchi Souzou. These two games just make me think about life and existence in general and they have a universal message or messages to share with the people of the world. I'm not enlightened enough to figure out what the messages are but part of the fun is trying to work it out. Gaia Gensouki is rare in the sense that it has a relatively large cast of major characters AND they are all important to the plot (instead of being there just for decoration). Also, I think it's one of the rare games that gave a sense of innocent adventure (Grandia 1 PS1 is also similar), as opposed to going on an adventure for the sake of saving the world. The fact that they travel to real life locations help support the adventure theme. Story-wise, I still don't fully understand it. I just know it is deep. In Internet terminology, I guess it is called "feels", which is what this game gave me.
Memorable moments:
Plot-progression via floating on a raft with the princess.
The fact that every town has its bad side (e.g. the contrast between Freejia's flowers and its participation in the slave trade).
The Nazca Plains and Sky Garden sections (and the Sky Garden dungeon music).
I particular liked the dungeon design of China's Great Wall.
The kid whose parents suddenly turn into ghosts, and him handling it surprisingly well.
The pig's selfless sacrifice.
The Pyramid is a suitably epic last dungeon.
It turns out that by collecting all the red jewels (and the slave trade throughout the entire game is a part of it), you're basically helping the bad guy from Soul Blader. This would be more of a memorable moment if I had played Soul Blader before this game, but I didn't.
Rockman X (Mega Man X) - A major part of the appeal of Rockman X is seeing the technical advancements from the Famicom versions. The heavy metal inspired soundtrack is also neat (my taste for heavy rock/metal began around this time).
Rockman X3 (Mega Man X3) - I think I like this game for two reasons: being able to play as Zero, and I like the guitar synths here better than the prequels.
Seiken Densetsu 2 (Secret of Mana) - I consider this game a fairy tale in video game form. This game you give to children (instead of reading fairy tale story books) to help them sleep at night. Hiroki Kikuta's soundtrack is also a major reason why I love this game so. Gameplay wise, the fact that party members can get trapped in corners is annoying (fixed in Seiken Densetsu 3) but enemies are easy to run away from (broken in SD3, why).
Memorable moments:
Haunted forest to witch's castle section (I quite like forests, see FF6).
The evil temple/shrine locations and music. The goddamn music man.
The Ice Palace and the lovely music.
The Upper Land with 4 seasons sections is pretty neat.
The surfacing of the Grand Palace and the second overworld music (the tolling bells one).
Pure Land and Randi communicating with his parents for the last time.
The Mana Fortress, the battle with the Lich (the goddamn music man), and the final battle (massive screen-filling sprite).
Super Metroid - It's all about the atmosphere. There's been many Metroidvania games since this game, but as far as freedom of movement goes, none can beat Super Metroid yet.
Memorable moments:
Landing on the quiet planet with only the sound of rain and thunderstorms.
Inner Maridia (with the two Maridia music). Yep, my obsession with underwater.
Cute Baby (not baby anymore) Metroid sacrificing itself to help you in the fight against Mother Brain.
Tenchi Souzou (Terranigma) - The other game filled with soul and feels. Good cast of characters, deep story, and all locations based on real life settings. Magic system is unfortunately pretty meh and easily ignored.
Memorable moments:
Arriving on the barren red Earth world map for the first time.
Assisting the cute Leim (the lion cub) on his quest. And the transition from " (only played here).
Getting trapped in an ice cavern with a deer. Escaping the cave but forced to leave the deer behind. Sad. Corpse of said deer remains if you come back later.
After the resurrection of humans, Ark losing the ability to communicate with animals. Very sad. Underrated sad.
After Ark stays at an inn and wakes up, finds entire town in decay, and the zombies even more decayed. It basically becomes a survival horror game. I like horror in games that aren't meant to be horror games. The interior music and exterior music (tolling bells + X-files whistles) supports the spookiness/creepiness of this section.
Towns that actually have Asian people (Neotokyo and the Chinese one). Neat.
That whole trippy shrine/altar scene.
Reunion with Leim (who is now a fully grown lion) in the sewers of Neotokyo.
On the ship set to self-destruct, male and female knight calmly accepting their incoming death, and selflessly gives up the escape transport to Ark.
"Resurrection of the Hero" and the plot progression here.
Ark returning to Crysta. After speaking with a random villager, the screen turns red, the villager turns into a malignant (but harmless) spirit, and creepy music starts. I avoid doing so.
Ys V: Ushinawareta Suna no Miyako Kefin (Ys 5: Kefin, Lost City of Sand) - Sue me but the Ys series seem pretty "overrated" to me. But I have a soft spot for Ys V. As usual, like most of the games listed above, the music is a big part of it. I also like the locations (ruins, forests, deserts, etc). Story-wise, I can't say because when I played the game, I did so with little knowledge of Japanese.
Zelda no Densetsu: Kamigami no Triforce (The Legend of Zelda: Triforce of the Gods) - Also one of the first games I played on the SFC. And since I already played the two Famicom games prior to this one, I was wowed by the improvements that the SNES offers. Story-wise it's nothing amazing but you're here for the open Zelda world and spelunking through the dungeons.
Memorable moments:
Climbing up Death Mountain.
Climbing up the Death Mountain's tower dungeon (I like towers. See FFUSAMQ).
Getting the Master Sword and the Lost Woods music turning into the standard overworld music.
Wallowing in nostalgia was fun but writing all this took longer than I thought so I'm just gonna list the rest.
SONY PLAYSTATION 1
Akumajou Dracula X: Gekka no Yasoukyoku (Nocturne in the Moonlight)
Alundra
Final Fantasy VII International
Final Fantasy Tactics
Gensou Suikoden (1)
Rockman X4
SaGa Frontier (1)
Valkyrie Profile
Vandal Hearts: Ushinawareta Kodai Bunmei (Lost Ancient Civilisation)
Xenogears
SONY PLAYSTATION 2
Breath of Fire V: Dragon Quarter
Guilty Gear XX: The Midnight Carnival #Reload Korean Ver.
Metal Gear Solid 2: Sons of Liberty
Rockman X8
Shin Contra
Shadow Hearts (1)
Valkyrie Profile 2: Silmeria
Wander to Kyozou (Shadow of the Colossus)
Xenosaga Episode I: Der Wille zur Macht
Umm, there aren't any PS3-era games not because I don't like those games, but because I haven't played them...