In my case I was trying to find a nice sitcom on Netflix and came across a J-drama initially - Good morning call, I liked but didn't love it, then I saw there was a K drama- Playful Kiss, I completely loved it and since then can't stop watching asian dramas.

Although now Playful Kiss isn't my favorite drama of all times, it does hold a special place in my heart as it brought me into this unique wonderful world of asian dramas.

My most favorite ones are surely the korean dramas, but I also watch Japanese,chinese, tawainese and also some thai lakorn once in a while.

What about you chingus?

A classmate once carefully asked me if I knew anime during art class so I said Yes I do xD So we became friends and she introduced me to Korean dramas, my first one was You're Beautiful (And first Kpop song was MBLAQ's Cry), same here it's not one of the best I've watched but it holds a special place ^^ But since I'm Chinese I often watched chinese (or chinese dubbed) dramas with my mother and granny when I was little xD So you could say my first Chinese dubbed Korean drama was Stairway to Heaven lol

My favorite dramas are also Korean ones ^^ I also watch Chinese dramas and Japanese only if Im in the mood for it. I haven't tried Thai dramas yet, but I will certainly try in the future ^^ 
Since I was  a teenager going to local art-house theater:... Into Hong Kong Kung-Fu first, then Japanese classic and last is Chinese new wave films
** Firsts: Drunken Master (Jackie Chan), Seven Samurai (Kurosawa), Raise the Red Lantern (Zhang Yimou)

As for dramas and Korea:
A few years ago, I was on Netflix looking for something similar to Jane Austen, North & South, Robin Hood series.... Which led to movie
** Firsts: ---> A Moment to Remember ---> then to movie Man from Nowhere --->  then to show Warrior Baek Dong Soo ---> then to Chuno ----> then to addiction, w/ Jang Hyuk as my first love and drama-stalking him!

A few years later, I rarely watch K-dramas now, prefer C-dramas ... really getting into J-dramas ... and my guilty pleasure is lots of lakorns (prefer older ones).
rarely watch Taiwanese... Have yet to try a Hong Kong Drama (would love to watch ones from 1980's w/ legendary HK actors: Tony, Leslie, Andy)

well my first series was boys over flowers, and appearntly I found out that this movie ha ji won played in 100 days with mr arragant was it?  was my first movie. I watched that movie cause of a sailor moon spoof in there lol. but think it was boys over flowers then playful kiss. al i did was bought dvds. I got into more kdramas in late dec 2013/2014 and watched more and more. I think I am now a kdrama addict
From a college friend. We're taking a break from studying, and she showed us this drama called "Full House". I insulted Rain's character all the way, but I ended up being hooked.

I started watching Chinese and Hong Kong movies (mostly martial arts with fantasy elements, or comedies, which is why I have a very high level of tolerance for splapsticks, having grown up with Stephen Chow's movies) even earlier, ever since I was kid, because they're available on local terrestrial channels; the same with Japanese dramas.
My first kdrama was IRIS. I saw it on tv and it was interesting as i was still a kid and i loved action. After that i would keep on watching kdramas that came out on tv and jus watched through the episode even though i haven't seen the first few eps. Gradually i got even more interested and watched them online.
I started getting into KDramas quite recently this year in late June (so around 6 months ago). My best friend got into KDramas last year and recommended Descendants of The Sun to me (It was widely spoken at the time) but when I saw the episodes were an hour long each, I was like heck no. Then at school, my friend introduced DoTs to another and she started getting into it and introducing it to others. I realized DoTs was very popular but then I got into Running Man and started binge watching it. I forced myself to endure an hour of a show for the first time & I actually really enjoyed it so that opened up my whole view and aspect of KDramas. I really liked Joong Ki in Running Man and so I decided to give DoTs a turn. I completed it in 2 days and was obsessed with it and that led me to watching other KDramas :) 
I never used to watch TV, but i was in a foreign country and i was so sick i couldn't walk for two weeks.  I turned on my TV for the first time and checked out what was on.  All the american channels had some kind of CSI, NCIS, Homicide nonsense.  I hate these kinds of shows.  I couldn't understand what was being said on the local channels.  The australian channel had stuff about country life.  The movies were all B grade action films. and the rest was all "news" also nonsense!  I kept flicking through channels and KBS World came on.  Jang Keun Suk was so pretty.  I liked all the side characters.  I finished watching that episode and youtubed the rest.  Then I watched "You're Beautiful" and "The King's Face" I went surfing and googling trying to find other good korean dramas and now it's all I watch (with the occasional Japanese or Chinese drama thrown in.  The really good part is all my Khmer friends watch them too, so we had something to talk about.
Master's Sun, story's on my profile :)
I got tired of American shows,and wanted a change....Now I love Kdramas,Twain,Thai,and Chinese wayyy more than American shows....I'm a die hard romantic fan,and all American shows are is sex and no love.....Kdramas most of the time they rarely kiss let alone have sex,but the chemistry be on point*_*  
My mom's always watched Asian dramas (often dubbed in Vietnamese) but it was never my thing even though I'd watch with her from time to time. It wasn't until I got into kpop did I decide to check it out. Around the time I got into kpop was also the time The Heirs was really popular. Idols kept making references to it, so I was naturally quite intrigued and wanted to understand the references. I then ended up marathoning The Heirs back in 2014 and started watching more dramas from there!! Like Playful Kiss for you, The Heirs isn't one of my favorites or anything, but it holds a special place in my heart. From there, I got into jdramas as well. I don't really see myself branching out beyond Korean and Japanese dramas though tbh. 

I also don't think I'm as addicted to dramas as some users on here since I'm really picky about what to start to begin with and end up dropping a bunch after the first episode, but I'm definitely the most addicted out of all of my friends!
I'm also the same! I remember that my mom used to watch Meteor Garden because of F4 (they were really famous) and you could say that my interest in drama started at that time but i didn't follow it through. When we moved to new house, there were still some old drama dvds that my mom bought and then i became so addicted. I decided to rent a lot drama as internet didn't provide drama site like now. The rest is history.

I start with k-dramas but i have watched so many and i can already predict the endings already LOL.
Nowadays c-dramas is really good such as Nirvana in Fire (Hu Ge as my profile picture!) and sometimes when i'm bored, i watched J-dramas because they are totally different.
In high school a classmate (that I never really spoke to) was talking to my friend and I about this drama called.... Boys Over Flowers lol it was fun talking about the drama together, but while I got dragged into kdramaland, by friend and classmate lost interest..... this was 6 years ago..... 
I've ventured out to Japanese and Taiwanese, but I find Korean the best. 

Mine's a very strange and random introduction to the drama world.

I'm a big fan of Adele and in 2011 when she released set fire to the rain, i was searching on Youtube for a lyric video. I came across a fan made video of the Japanese Movie Koizora to her song. As someone who had never watched any anime or anything asian before, i remember being really intrigued by this cute asian guy with blonde hair. Anyhow, I watched, cried and I fell in love with the movie. I, then done some research and started watching a couple of japanese and taiwanese dramas until a few months later, i discovered my first ever korean drama, You're Beautiful. 
Been in love with them ever since.

So I guess i can thank Adele for destroying my social life LOL Weird right?! ^o^
My friend strongly convinced me to watch All About Eve. Totally fell in ❤️ with it. So,after more or less 10 years of Kdramas...

My Kdrama addiction is slowly getting replaced by  Chinese dramas addiction. 

i accidentally chanced upon Empresses in the Palace on  Netflix while looking for another Kdrama and the rest is history.