Level 10 features Goromorgs, lethal forcefield wizards that you fight in groups.
In II, the 'swarm' type enemies such as the insects in Keelbreach Bog are EXTREMELY fast in both movement and attack speed, have high evasion, can only be hit during a certain part of their animations, and hit quite hard, especially on the roughest Difficulty.
Paranoia Fuel: A given, being a dungeon crawl. Worse without a torch. And the telltale stomping of marching skeleton warriors on floors just above or below you is very unsettling, at least to first-time players.
Special mention to the Pillars of Light level for the spiders. They are everywhere, and they're decisively powerful (and venomous) enough to be full-blown Demonic Spiders when first encountered.
Level 6 leaves you trapped in a large, open, poorly-lit expanse with a lone ogre lurking somewhere, nearby or far away. You'll feel the wet breath on your back till you finally bring yourself to seek it out and kill it (which you don't have to do, but...well, decide if obtaining a Tome of Fire, which gives your Mage 3 fire skill points and +10 Resist Fire is worth hunting it down, as it carries the gold key).
Level 9 leaves you in a series of convoluted twisting hallways filled with Ice Lizards, dangerous late-game threats that move relatively quietly and like to attack from behind. Good luck getting cornered by more than two. And they respawn.
The warning next to the entrance gate leading to that area sums it up pretty well. "Temple Grounds. Trespassers will be hunted down." Open the gate and find another sign: "You have been warned."
The sequel has Mimics that any chest has a chance to be, depending on how many chests you've opened so far. Once you encounter your first, you're sure to be terrified at the idea of finding more.
That One Level: While all the levels are pretty hard, one secret dungeon on Level 3 has attained a level of notoriety for being filled with Slimes, high-health, low-experience monsters that spread disease to your party members and can attack through bars. It isn't even needed to attempt this dungeon unless one wants a crossbow and one of seven optional hidden treasures, collected for a measly achievement, but it's borderline impossible if attempted right when the player is at Level 3. Later in the game, the player obtains a map to access this dungeon, if they didn't find it already.
Level 3 in itself is a very notorious level for the abundance of spiders.
That One Puzzle: While there are several tricky puzzles in the game, the rotating teleporter puzzle found on level 3 is the first to leave a lot of players stumped. And when they finally figure it out, it's still hard to get right.
The "Trails of Thought" puzzle on Level 4. A room made up entirely of floor plates and teleporters. The teleporters move whenever you step on a floor plate. There's a specific path you have to take to make your way to the door, and it takes many tries to get it right.
The trick to the room is that every time you take a step, all teleporters next to you will turn from on to off or visa-versa. If the space is not touching an active teleporter, it will turn into a dead end the moment you step onto it. In general, making sure you keep stepping onto a platform that is next to a teleporter makes the puzzle much easier.
Anyone familiar with the Lights Out puzzle will have a head start in figuring it out.
Level 8, so much. Better hope your heroes Resist Shock pretty well... (Then again, it's technically optional... but who'd pass up a sword like that?)