Big Bang's My Girl. I use to love them and they got me into K music in general. Oddly enough, I rarely listen to them nowadays, but my taste has matured quite a bit.
Big Bang - listened to their concert on Drama Fever and I was hooked when I heard Blue.   For my sister, she became a fan when she heard Big Bang's If You. I even went to a Big Bang concert in Tokyo - they are amazing performers as a group and as soloists (all 5 - XD).  
SuJu Sorry Sorry :')
SNSD - Genie
I've even got the instrumental as ringtone ㅋㅋㅋㅋ

I was Super Junior trash. Now I'm EXO trash. 
BTS - Fire was the first kpop song I liked but then I got into EXO which made me get into other kpop groups
Maybe not "made crazy" about K-pop but definitely i'm into k-pop because of EXID :P
My first was Topp Dogg but I'm major BTS and B.A.P. trash now
BTS - Boy In Luv started it all for me
Big Bang's Lie, although the first Korean song I heard was probably Loveholic's Shinkirou (a song from the anime Black Blood Brothers). #VIP
Super Junior - Mr Simple
I was watching random videos on you tube when I came across it. I decided to give it a try and I loved it!!
super junior and snsd omg :'))
So compared to all the other answers my answer is a bit small. The first group I've ever listened to was Monsta X. I heard them when they first debuted, and I have loved them since! Even more after I watched the show No mercy.