And by retro I mean one that's just quite old or iconic for that time, where if you said you started watching it people would look at you in surprise

I watch a lot of older dramas but maybe Flower Boy Next Door? I've heard it was popular when it aired and I love it a lot but people rarely mention it or like it now.

Ruler of Your Own World, from 2002. This has never been as popular as stuff like Winter Sonata or Autumn in My Heart and the likes, but supposedly it had cult following in South Korea.