These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Crowning Music of Awesome: The remake has too many to list, but three that stand out are "War Demon" (Boomerang's theme), "Destruction of All Creation" (Mother's theme), and "Windward Birds" (Zeik Tuvai's theme)
Demonic Spiders: Raidbusters. Normally, they'd be easy to take care of, only having lots of HP and an above-average strength on their side. But they attack at a point in the game when the party is split up, and always attack in pairs (plus sometimes they'll arrive with a Gremlin who can lower your defense. Jack will have less trouble, since he can just one-shot one of them with Meteor Dive, but Rudy and Cecilia will be in for a world of hurt.
Game Breaker: In the remake, Rudy gets his Gatling Raid cartridge a little more than 1/3 into the game. Use with 18 bullets and every non-optional boss in the game goes down in one turn. Combine with Lock-On Active and its auto reload for pure bullet spam.
This method is practically a requirement for beating the optional end-game bosses without running out of resources in every battle.
By putting Great Booster on Rudy, casting Offense Zone on the battlefield, and Fragile on the enemy, it's easily possible for Rudy to do over 100,000 damage with Lock-On (even more with Lock-On Plus). The only other one who comes close is Jack under the same conditions with Accelerator + Laser Silhouette and the most I've seen that do is 75,000. Most battles don't last long enough to set up both of those guys for that much damage.
Play through the game until the Volcannon Trap mission, which is when Jane temporarily joins you. Go fight Rat Monkeys at the beginning areas and have her steal MP Repair skills from them. Not only do they sell for a whopping 999,999 gella (ONE will pretty much take care of your money problems for the whole game, even including the 600,000 gella required to completely rebuild Adlehyde), but the skill itself restores MP as you walk, which is insanely helpful for characters like Jack, who has very little MP and very expensive special attacks (until they're leveled up anyway).
In the original PSX version, there's a bug that lets you very easily duplicate items. All you have to do is have your first two characters use the same expendable item (Heal Berries are easiest), then have the third character switch the location of that item with something you have one of. At the end of the turn, the game deducts two from the number of the item in that slot... which, since there was only one, takes it from 1, to 0, back around to 255. Use it on apples and you can effortlessly max everyone's stats, use it on Crest Graphs and you can get all the spells easily, use it on Secret Signs and Jack will only ever have to use 1 MP for any of his skills, use it on Goat Dolls and abuse the ability to re-equip your characters in battle and nothing will ever be able to kill you...
Iron Woobie: Bartholomew. In both versions, he survives a plane crash that he was forced into flying against his will and also survives a shipwreck. The latter is much worse in the remake.
Moral Event Horizon: Alhazad turning an entire town's population (save one blind girl) into monsters, and attempting to do the same thing to Jane's town. Keep in mind that the majority of her town's population are orphaned children.
Nightmare Fuel: Pretty much anything involving Mother. A fleshy pulsating thing, she's an Omnicidal Maniac who wanders the cosmos consuming countless star systems (making her a proto-Jenova). By far the creepiest scene with her is when Zeikfried is teleported to the destroyed Photosphere as the result of falling into a black hole. only to find the veiny, slug-like remnance of Mother that proceeds to rear up and consume him while cooing about how much she loves him, accompanied by sickening crunching noises.
Not to mention Alhazad's true form. Or his special "Demon Seed" parasite that painfully turns living things into monsters. Made worse in Alter Code F. In the original, we only see a dog transform from the Demon Seed, and its instantaneous. Here though, we get to see the Wanderer who was helping Jane's town scream and convulse in pain before finally transforming. Brr...
Player Punch: The revelation of Lady Harken's true identity.
Scrappy Mechanic: Instead of learning Fast Draw techniques right away, Jack instead learns Fast Draw "hints" in the original game. He then has to use the technique repeatedly until he actually learns it (using an unlearned technique causes him to just use a normal attack.) This unfortunately leads to a lot of grinding, as learning a Fast Draw can take dozens upon dozens of usages of the unlearned technique. Fortunately, the system for learning Fast Draws was changed in the remake.
Tear Jerker: The backstory of the Maxwell family that Magdalen tells in the remake.