1. my name - do kang jae

2. the glory - park yeon jin

3. Arthdal Chronicles- Tagon

4. EviliveBoth the leads

5.Strangers from Hell -Seo Mun Jo

6. Bossam: Steal the Fate - FL's FIL I liked that he was calm and smart, not like those hysterical screaming villains

7. Under the Queen's Umbrella - Queen Dowager. Acted so well and chemistry with FL was on fire, so intense scenes!

Bonus, since he was more like an antagonist than villain:

Bloody Heart - Park Kye Won, can't call him a villain, he was more like an antagonist. First, his acting and charisma,wow. Second, the character had strong and reasonable motivation for his actions, not just evil being evil. Plus, his non romantic chemistry with FL, he overshadowed ML for me haha

8. Any of Three Kingdoms adaptation for example: Three Kingdoms 

Cao Cao

He may be a traitor, but he's the coolest guy in Three Kingdoms. He may want to recruit Guan Yu to his side but he doesn't use force. He may want the throne but he doesn't kill the puppet king (iirc). He has this weird standard of morality but that makes him somewhat cute.

Sima Yi

No one smarter than Zhuge Liang/Kong Ming in Three Kingdoms but Zhuge Liang choose to be loyal even though the one he's loyal to choose to believe another advisors. And no one as scheming as Sima Yi. No one knows the future of their own children and grandchildren, but Sima Yi may build the path for his grandchildren to become the emperor. A great ancestor.

9. The Princess' Man (where he becomes the villain)

Sejo

His grandfather wants him to be the king because he helps his grandfather in war and land expansion. His father wants his older brother to be the successor because this older brother helps creating Hangul so his brother becomes the king and he let the brother becomes king until his death. After that he killed his way to the throne. I just love double-standard villain.

 Ahn Sarang:

Can explain what you mean by "loved"? Admire villains themselves or hate them and appreciate writing, or anything else? 

Sorry for responding late. Whether you loved the actor's portrayal of a character or felt for the villain because of their back story.

Eg. Weak Hero Class 2 - Na Baek Jin's back story was that he was an orphan and was bullied.

Strong Girl Namsoon - Ryu Shi Oh, a lot of viewers felt bad for his character because he actually cared and protected the female lead.

Mouse - I loved Lee Seung Gi's portrayal of his character