The Mega Man series is well-known for its challenging enemy designs and placements where every enemy is determined to hit you at least once before dying... which they usually manage to do when you're not expecting them.
Metools/Mettaurs in the Mega Man series are near-invincible mooks with their unbreakable hard hats, which they hid behind indefinitely and only peek out to attack, meaning you have to time your shots perfectly to nail them before they duck back under, and avoid being hit. A goo-shooting variation found in 10 is especially annoying since they're much better at hiding under their hats.
Made even better in 9, where you at one point encounter Mets disguised as extra lives. Until they start shooting at you. Thanks, Capcom, you're a pal.
The Sniper Joes and their cousins are worse, as they pack a much bigger punch than the Mets with the same invincible body armor/shield and limited time frame to counterattack.
9 takes some of the scrappy out of the Joes with several special weapons, including Laser Trident; it pierces their shields, and you only need three to put each one on ice.
Crashman's stage in 2 had those floating cylindrical robots called Tellys or Pipe Bombers endlessly spawning from pipes on the sides of the screen, which really messed you up when riding the Floating Platforms. Stage 4 of Dr Wily's Castle took this to near Demonic Spiders level with moving platforms over Spikes Of Doom. The Tellys also appeared in Heatman's stage, where they could knock you into a Lava Pit.
The Mega Man Zero games brought them back in the form of an exploding variant called the Tellybomb! There are several areas where you need to use your Z-Saber to knock them into cracked walls in order to blast through. Good luck getting yourself positioned correctly to hit them in the right direction without getting blown up accidentally, though...
Don't forget those horrible birds ("Pipi") in 2 that would drop eggs full of mini-birds on you, usually making you fall off a ladder, or into a pit.
Spines/Gabyoalls are a special pain. They move left and right along the surface (usually speeding up when being at the same altitude as it is) and can be destroyed only with some special weapons. Just try Concrete Man's Stage or Elecman's stage, using no special weapons or items. Not to mention their location which is often on tiny platforms which have to be jumped on.
The worst kind is found in 10 which actually shoots stuff at you when hit. Also, these types are slightly taller than their brethren from previous games. This doesn't make them significantly harder to dodge, but it makes you wish they were shorter so as to invoke Denial of Diagonal Attack.
Moles (slow-moving drill enemies that constantly spawn from the floor and low ceiling in large quantities) found in Mega Man 2 and 10, when you don't want to farm them for items.
In general, pretty much every enemy in Mega Man is designed to either damage you or knock you into a Bottomless Pit, especially if they rise from there.
For that matter, any Battle Network enemy that jumps around the battle area, or with an attack that hits several squares/rows/columns, one at a time or all at once. And Lan help you if they do both, you can kiss your Busting Rate goodbye. They become downright demonic if you have to face two or three of them at once.
From 10 we have lockers. Yes, lockers. They only appear in one stage, namely, Strike Man's, but if the background looks like a locker room, be careful. These things can open right in your face, which is annoying enough, but then they shoot at you.
Mega Man ZX Advent has what might just be the best example of this trope. In the floating ruins, there are green enemies called Invises that turn invisible. This doesn't prevent them from causing Collision Damage, and they still move around, albeit slowly. When they finally do turn visible is the time they shoot at you. Did I mention the floating ruins has wind that blows you around, and lots and lots of Bottomless Pits?
PULSE. CANNONS. Only found in the Floating Ruins, these are truly the ultimate cliff-droppers. They don't damage you, but if they are on the same screen as you, they will shoot an unavoidable, super-fast homing shot that basically fries your jump button temporarily, meaning no wall-jumping, no flying, no nothing. And when the effect wears off? They shoot another one. Worse still, the effect also prevents you from climbing poles as Rospark, and the first part of the level requires doing so, and if you're on a pole and you get zapped, you will almost certainly fall to your death. Oh, and did we mention they're INVINCIBLE?!
The only thing that can kill them is Bifrost's Ice Bite attack. But good luck even getting Bifrost up to them...
Battle Network 4 has two exclusive to the game; Cirkill and Spidy. Cirkill moves in a circle around its side of the field, taking shots when level with you. Coupled with other viruses, the shots become very hard to dodge quickly. In any battle, a Spidy's first move is to teleport into your side of the field and chase you around. They also lay down webs which hurt you when stepped in.