Zelda: Ocarina of Time and way too many later games: Insta-fail stealth sections.
Zelda: Majora's Mask: The first 3 day cycle, which even speedrunners haven't been able to skiip. (Arbitrary code execution has been found, which makes it possible to skip almost the entire rest of the game, but there's still no way to skip the first 3 day cycle.)
Chrono Trigger: There is one part where you literally have to mash a button in order to proceed.
Dragon Quest 6: A part where you have to follow someone, and if you get seen, you have to start over.
Also, in SaGa 2 my least favorite part is Ki's Body, which is a fairly sizable dungeon area that has no treasure (except for the excavation point added in the remake that has a random stat boost potion (which can be defense)). Even worse, this comes before the point where, in the original version, you can use glitches to skip the rest of the game.
Final Fantasy 3 has one part where you're in a huge world that's mostly water, and you need to find a specific small island in order to progress through the game; the world is big enough that (in the original game) if you cast Sight, there will probably be no visible land on the map that appears. On the other hand, this part does feature ny favorite music track in the game, which sadly goes away after you complete the next dungeon. (With that said, the game isn't *that* great; both FF1 and FF5 are better, as FF3 has poor normal enemy design.)
Final Fantasy 1 has, right before you get the freedom to explore the world with an airship (at which point many interesting gameplay options open up), the dreaded Ice Cave, which is notorious for its difficulty. For example, remake versions feature the dreaded "Enemy Wins First" effect, where a group of Mages ambushes yor party and burns your entire party to death before you even get a turn. On NES, that particular encounter isn't as bad, but you still have to worry about instant death (though at least you don't have them using multi-target instant death often, whereas they do in remakes if they get a second spell of). I wouldn't mind this as much if this were saved for end-game, but having this happen in a dungeon that gates many fun gameplay option isn't nice. To make things even worse, once you get the treasure you have to *walk* out of the dungeon, as you do not yet have the ability to teleport out of the dungeon.