Klap Trap (Donkey Kong Country): Adorable design that serves a very effective enemy function. The snapping sound effects in the SNES games were done by a Rare sound guy actually slamming his jaw shut. I hope it didn't mess with his dentistry, because it sounds so much better than the stock cartoon sound effects used in DK64 and afterward
Rockroc (Donkey Kong Country): Invincible zombie crocs that disguise themselves as rocks and ambush you at high speeds in dark mines! Incredibly memorable, unique, and challenging.
Kutlass (Donkey Kong Country): A regular platforming enemy with a backstory (via the manual): He allegedly mail-ordered cutlasses to get on board with the pirate rebranding the Kremlings went through in DKC2, but he had a tiny TV, and they wound up being way too big for him, which he was excited by! And this translates to gameplay, as he's extremely deadly, with speed and a huge attacking radius, but when he misses with his oversized swords, he struggles to pull them out of the ground, giving you the opportunity to attack or flee. It's honestly one of the best overall enemy designs I've ever seen (I'm kind of regretting not putting it even higher), and I think it only got slept on because gamers generally don't think of DKC for its enemies.
Army (Donkey Kong Country): I really like armadillos, and they don't get a ton of representation in gaming. These also make really cool enemies, becoming both very fast and resilient when they curl up. They're one of the few enemies that give Donkey Kong an advantage in the original DKC (where Diddy outclasses him in about 95% of situations), as he can defeat them with one stomp when curled up.
Red Arremer, Ghosts 'n' Goblins series.
Chain Chomp (Mario Series)
Cacodemon (Doom)
Dragon (Adventure): These guys were discussed earlier in the thread. They occupy a similar niche in my mind as the Pac-Man ghosts, but their behaviors are more interesting in my mind, especially the way they interact with the bat, and how the game doesn't actually end if they eat you...you're just left helpless in their gullet.
Spiny (Super Mario): If Lakitu threw Goombas, it wouldn't be half as intimidating as it is. These guys establish a classic enemy archetype: harmful to stomp on. But Spinies do even more than that! In the first SMB, they also can't be beaten by bashing blocks beneath them, showing that it's not just the spines; they're all-around tough. They drop from ceilings, they supply one of Mario Kart's most notorious items...they don't get nearly enough credit.
Lakitu (Super Mario)
Regenerators, Resident Evil series
Metroid (Metroid Series)
Space Pirate (Metroid): They may be nothing too special in the 2D games, but they manage to be both some of the most varied and challenging threats of the Prime games, and their primary source of comic relief. Their logs, their constant horrific, backfiring mad science experiments, and their utter panic at Samus (and Dark Samus)'s rampages are consistent sources of amusement. And they have this
tune!
Bumpty (Yoshi/sometimes Mario): One of the dozens of reason Yoshi's Island is amazing is that plain old damage, while still not good, isn't the be-all, end-all consequence of enemy encounters. Bumpties work beautifully with the icy climes they're found in, not dealing any contact damage but...bumping Yoshi, leaving him more vulnerable to environmental hazards. They also have so many behaviors and expressiveness, sliding across ice, cartoonishly struggling to fly, and even kidnapping Baby Mario (it took me a long time to realize they did this, because, again, they're usually poised to knock you into pits or instant-death hazards rather than regular damage).
Monkey/Grinder/Ukkiki (Yoshi/sometimes Mario): Similar to the Bumpties, these guys show off more personality and a wider range of behavior than should be possible in a 16-bit platformer (heck, I'm hard-pressed to think of platformer enemies that compete with them.
Sting/Manta Rays (Star Fox): Sector Y is the coolest level in the original Star Fox. It's a literal space ocean with massive schools of rays. Red ones are being mind-controlled by Andross's army, and shooting them turns them blue and they drift peacefully on their way. Extended segments of the level involve one (or sometimes two, a variation that seems random) massive mantas drifting around peacefully in the background, and if too many of your stray shots hit them, they become aggressive and hit you with a highly damaging (probably) unavoidable attack. Turn away all of the little red rays without aggravating the big ones, and a space whale flies in and gives you a whole ton of power-ups. It's a fantastic sequence, and the rays play to the strengths of the limited polygonal graphics, showing off more animation than the game's various mechanical enemies while still portraying the creature in question reasonably well.
Colonel Bahamut's Mutated Minions (Contra): In one of Contra Hard Corps' possible final stages, the alien biological samples captured by the rogue Colonel start contaminating his base, transforming his soldiers into these hideous alien chicken-beasts that start sprinting and hopping wildly through the stage. It's not only some impressively groteseque spectacle for a 16-bit game, but they make interesting and dangerous foes, taking quite a bit of abuse and moving erratically. Further selling the chaotic horror of the moment, they're not really out to get you, and indeed, if two of them collide, one will devour the other.
Dry Bones (Super Mario): Another classic enemy type (actually beaten to the punch by Castlevania's Blood Skeleton), with the adorable charm of Mario character design attached. They're rarely a giant threat, but they shake things up with their persistence and immunity to fireballs (except in Paper Mario, where they're bizarrely extremely allergic to fire), and while it took them a while to invade the 3D platformers, they're probably at their most disruptive there. Popular enough to be a semi-regular playable character in sports and party games.
Li'l Mouser (Yoshi): Maybe not as expressive or interesting as YI's best enemies, but these guys quietly are very involved for such a minor enemy. They play the "pest" role perfectly, and again emphasize the variety of ways enemies can mess with Yoshi. They often pop in and out of holes and passages and steal your eggs, which also defends them from retribution (since trying to lick one carrying an egg will result in them dropping it, rather than harming them). They sometimes don skulls and try to look more intimidating, and they have a network of tunnels that are often just there for flavor, but sometimes lead to little caches. There's way more to this enemy than you'd think at first glance.
Piranha Plant (Super Mario)
Boo (Super Mario)
Imp (Doom): The Caco is cooler, but these guys are iconic as well. Their original design is classic, and they're very expressive in the modern games, helping sell Doomguy as a terror to demonkind.
Shy Guy (Super Mario/Yoshi)
Spike Top (Super Mario): Was it silly to vote for these guys AND Spinies? Probably, but as any Mushroom Kingdom zoologist will tell you, these are very different critters! They're both fireproof AND stomp-proof, making them a stern challenge to your typical plumber (or they would, if their most prominent appearance wasn't Super Mario World, where Yoshies and capes are everywhere). They can also crawl on all surfaces, and all of these properties together make them some of the most interesting critters in Mario Maker. Their numerous defensive attributes also translate very well to the Paper Mario games, where they show up a lot.
Lynels (Legend of Zelda): I guess I voted these guys lower than I thought. Still shocked they didn't make the list...I thought they were such a staple of Breath of the Wild. I guess more folks associate the development from "complete terror to avoid at all costs" to "source of fantastic loot" with the guardians, which is fair, but Lynels were just such thrilling encounters throughout the game (maybe it's because I enjoy grabbing a nice, really strong sword over the guardian parts). Their role as gatekeepers to more advanced locations in the original game and some of the other top-down titles can't be totally dismissed either, but it was definitely Breath of the Wild that landed them on my list.