Which drama would you recommend to a person who has never watched any of them and who is not particularly interested in them ? I'm trying to convert people xD I'm thinking of something which is not "weird" for someone new in Dramaland, compared to a basic american serie for exemple...
Hana Kimi 2006/7 Japanese version is a must see if you are into comedy. It's lightehearted fun :D
Good luck in converting people. I guess J and Kdrama is something you either can't get into or you love it with crazy passion. There seems to be no middle ground. That's why I have no friends in real life or my family who watch these dramas but it would be great if they did so I can share my drama passion with them...but sadly no.
City Hunter - for action Shut Up: Flower Boy Band - for teenage life Lie to Me, or Protect the Boss - for RomComs... I know they're not the best dramas, but most romcom dramas are pretty "weird" for Americans, those are some of the most normal ones I've watched. Rich Man, Poor Woman - business/light-romance A Gentleman's Dignity - older people romance 9 End 2 Outs - 2 best friends turned into lovers, rom-com Those are some of the most normalish/relatable drams that can be compared to American shows that i can think up of. Though... they also might be weird. I don't know, my weird meter has diminished greatly ever since I became addicted to dramas :P
I converted three of my friend with "Personal taste" recently. It's lighthearted, nothing weird and LMH is drop dead gorgeous.
It depends on what the person likes. If I were trying to convert someone who would like romantic comedies, I'd choose Coffee Prince.

If I were trying to convert someone who'd like history, I'd choose Tree with Deep Roots.

If I were trying to convert a person who'd like a comedy that isn't just a romcom but has other elements as well, then I'd recommend History of a Salaryman. I also think this one would be not so weird in the mind of a person used to American dramas.

If I were trying to convert a person who likes something with fantasy elements I'd do either Arang & the Magistrate or Queen In Hyun's Man (and that would be my choice for someone who likes pure romance too).

Finally, if the person liked suspense AND didn't want to watch something too long, I couldn't recommend White Christmas enough. It's only 8 episodes. Also, if they are used to American tv and film then I think White Christmas would be perfect. It has really, really high quality directing. The soundtrack too would be familiar (with a lot of English songs) and the acting is really good. None of the characters are the goofy, over-acting types that you often see in Korean (or any Asian) dramas as stock clown-types. It is the most American feeling drama I think I've seen out of over 100 Korean dramas.

Honorable mentions, depending on the person's interests: Vampire Prosecutor (suspense, vampires, mystery), Reply 1997 (comedy, family, school) and Painter of the Wind (historical, art, aesthetic).

I hope this helps because I too am really interested in getting people converted to Asian dramas (well, mostly Korean because that is what I watch).
I suggested Marry stayed out all night to 2 of my friends and now they r in love with korean dramas but anyway it depend on person's opinion.
Romantic: Hana Yori Dango, Secret Garden, it started with a kiss, they kiss again
Action-Romance: City Hunter, IRIS
Funny: Hana Kimi 2007 version and Yukan Club
Thank you all ! You're a great help because as Witchgirl247 said I just couldn't discern what can be considered the most "normal" among the dramas I watched xD Also thank you for some dramas title I didn't watch/know, I'll check them out =D As for Winnie19 you have your response above, everything's possible ;)
Oh also another thing is, if they have a manga they like it maybe a drama. They might like to see it in a live action form :D
I think any romantic Korean drama will do. When I got introduced to full house I absolutely loved it and started looking for more like that. Thats because I'd never seen anything like that before in my country. But as somebody else has pointed out, it is either they will get obsessed with it or they won't like it. I tried to change many around me, sadly none liked anything romantic. Still I will ask many to start with coffee prince, full house, my girl. I've never tried anything other than korean though.. any suggestions?
I agree with what someone said earlier about Personal Taste....LMH really is drop dead gorgeous in that one. Anyway City Hunter is based on a Manga but not sure how faithful it is to the manga or how much the Koreans changed it. A very good action/romance series...good one to convert people as it has a bit of everything and more relatable for people who are not used to the 'Korean' ways.
For start loved kdrama try "princess hours" <3
Try Dream High maybe ? I refused to watch Drama at first but my friend kept pushing me to watch it so eventually I did and it gets me into drama.
most of my friends ended up loving dramas from watching Hana Yori Dango, You're Beautiful and Hana Kimi 2007