Final Fantasy 3 (Famicom): The Cave of Shadows. Not only is this dungeon long, it's filled with enemies that split when you attack them. Because it's long, using status ailments on them (which actually *work* in this version, unlike remake versions) isn't really practical, so you just go through with a party of 2 Dark Knights (can use weapons that don't cause them to split) and 2 White Mages (yes, you do need that much healing). Also, there's lots of mandatory invisible passages to find and navigate. (In remake versions, it's a bit more interesting when I play because I have a bard who keeps singing and using Souleater instead of normal attacks works well here, making things a bit more interesting.) I should mention that running away from everything (or at all) is not a good idea, because your entire party's defense drops to 0 and enemes deal double damage on top of that; this will result in characters being one hit killed. (Having a Master store power, which would otherwise be a reasonable strategy here, also has similar drawbacks with the character's defense, making it not viable.)
Final Fantasy 4: Magnetic cave. At this point, you are already down to just one real spellcaster, and his MP is severely limited, so you can't afford to use magic much (unless you're willing to use a lot of Ethers, which may be a reasonable idea especially in 3D remakes where MP recovery gets easier later on). Furthermore, any character with any metal equipment is permanently paralyzed in this dungeon (I've had game-overs due to this). In particular, Cecil is significantly hindered here, as he's normally a sword and heavy armored fighter-type; in 2D versions you could give him a bow (for reasonable attack damage) or a staff (minor free healing every round with a healing staff), but for whatever reason, the 3D remake took away *both* of these options, meaning you now have a useless character (and you're already down one member at this point, having 4 when a full party is 5).
Final Fantasy 6: Cave to the Esper world. It doesn't seem so bad at first, but then you get to one huge floor. On this massive floor, there are only 2 enemy types in random encounters, and *both* of them are undead, so battles are extremely dull at this point. (FF5 and FF6 have too little enemy variety in any given area, but it's usually offset by having different encounters on each floor, and there's 4 enemy formations in an area, so no excuse for having only 2 enemy types between the formations.)
I could also mention the stealth sequences in Zelda: Ocarina of Time and the button mashing part of Chrono Trigger, but I've talked about them at lenght before.