This song is what got me into power metal and metal in general:
The reason? I was rather impressed the way they could play so fast and still drench the song in melody instead of just "shredding" away as fast as possible wihout much melody to it. Also the guitar-solos got me hooked.
This song is what got me into death metal:
The reason? Speed, brutality, theme and one of the better growls I've heard. You'll notice that this particular singer growls in a rather unorthodox manner which use the vocal chords more than what is considered usual.
This song is what got me into nu-metal:
... What can I say. They're just fucking Slipknot. I just like everything about their music.
This song is what got me into Grindcore:
The reason? Well for starters they don't take themselves too seriously as a lot of other grindcore bands does, but stick with making "grindified" covers of more well known songs in a parodious spoof manner. It's quite a chuckle to listen too, though many of their songs are in german so you need to study up some german if you need to understand them.
Speaking of germans, here is one of the songs that got me somewhat into industrial metal:
The reason, aside from them being awesome in general is the fact that the song really speaks to me on a personal level, due to my pyromaniac tendencies. (I guess some kids stop playing with fire and pyrotechnics sometime in their life. I never did)
Here's another song in he industrial genre that sort of pulled me in:
It's one of my more "sinful" preferences in the metal genre due to the very fact that Deathstars should be the kind of band that I would dislike on principle, but for some reason I don't.
Here's a song that got me into heavy metal:
Aside from he obvious AC/DC influences, the song kind of had that "upbeat" feel about it that I liked about Through The Fire And The Flames by Dragonforce, but in another genre of metal.
These are he songs that are the most memorable for "sucking me in". Since then I have branched out a lot within the respective sub-genres of metal and explored the origins of the respective genres (once you find something good you just want to dig up more I guess).
Of course, my tastes aren't really exclusive to metal (even if it does take up a large area of my musical interest). Other genres include punk, classical music, jazz, techno and electronica. Pretty much anything besides hip hop and RnB (barely anything within those genres I find interesting, and most of it I find to be utter shit).
Pop-wise I tend to dislike most modern songs, bu I do like a few spanning from the decades of the 30's,40's,50's,60's,70's and 80's. Some songs because they are genuinely good, and some songs more "for teh lulz" and thus make them good in a more or less "silly" kind of way.'
Don't know if this gave the OP some real answers or not, but at least I tried to include motivations for each respective song I linked to where it was possible.