Healer - I do consider it as a timeless series, because the plot is very unique. Yes, romance-action genre isn't new, but Healer literally created a story which has equal percentage in terms of action and romance. It was all 50/50 which is a huge PLUS and I personally haven't seen it happen since Healer. Often we usually get 70 percent action plot and only 30 percent romance plot, which I am not a fan of and that's why K2 or City Hunter failed me.
Next, One Spring Night - It is slice-of-life series and I am sure years ago I wouldn't like it, but as I get older I tend to reach out for my age category stories and stories about struggles of life. The huge plus in this series that basically carries the show is the somewhat complicated romance? FL is in years long relationship having a fall-out with her BF when she meets ML and he boldly confesses to her and the whole process of them getting together is just so satisfying to watch and very realistic. There is not a single character there that isn't flawed and that's very realistic.
The third series would be Red Sleeve which is basically a sonata for yearning I would call it. It also contains very mature romance and the setting of the series is perfect as well. People who don't know the history and the nuances of it might be lost with the romance aspect or the political aspect of the story, but as someone who is studying Korean history it is a true gem.