or American song, i've seen It's Okay Thats Love and She was Pretty, had many famous American songs in them, i need more dramas like these that has a famous American song playing, its fun to here lol

Ha, there's a scene in King of Baking where they play a New Kids on the Block song.  That part of the drama is set in the 80's, I think, so it was weird but at least it made sense in terms of era.  Don't remember which ep, but it's one of the ones when the bad guy goes to a bar or club.

Coffee Prince had some, I think.  I can only remember the Kula Shaker song in this one basketball scene, which is neither American nor famous, but I recognized it.

Taereung National Village had a bunch of Wilco songs and stuff.  Again, not so famous, but very weird for me since things I listen to are NEVER in kdramas. (And I'm pretty sure the same director/music director was involved in both Coffee Prince and Taereung)

I'm sure there are tons more, but those are the ones that I immediately thought of.
The first thing that came to mind is Romantic Doctor Teacher Kim, which at one point played Material Girl by Madonna and Time After Time by Cindy Lauper. And A Wife's Credentials has Turn! Turn! Turn! by the Byrds. All of which you might not be familiar with if you're too young! But I'm old so I'm not knowledgeable in contemporary music, at all :D

(Oh, and since @zeamays has pointed out various "interesting" English songs in Kdramas, I can't help mentioning that the most surprising song that I've heard in a Korean drama is You Showed Me by The Lightning Seeds, in Evasive Inquiry Agency. Which is a British band and not really famous, I think.)
Shopping King Louis has Reality (Richard Sanderson) in at least one episode.
In Secret love affair the leads were fan of Piano Man so I think they played some version of it in some episode of the drama.