The "big 3" of 80's hardcore are Bad Brains, Black Flag and Minor Threat. There's just no way around it- these three bands changed it for everyone.
Of those three, Minor Threat is the only one that I really listened to in high school. It wasn't the whole straight edge thing, although it was definitely appealing because all of the people I was meeting at that time in my life were experimenting with various substances and none of them made it seem very glamorous. I also really liked their message of music for everyone- I obviously wasn't able to ever see them live but they helped spread the idea of more widespread all ages shows so kids wouldn't have to miss out on seeing their favorite bands.
Their messages were cool and all, but what I liked about Minor Threat was that they played it harder and faster than anyone else. And for a hardcore band their production values were out of this world. Even when compared to some modern hardcore bands, Minor Threat's songs still sound better. You can argue for days on end whether The Germs' "Forming/Sex Boy" was a better single and more influential on punk rock but there's no way around the fact that Minor Threat's sonic approach was untouchable.
Minor Threat was one of the first real hardcore bands that I listened to. I may be more into that gruff orgcore sound these days, but Minor Threat will always hold a special place in my heart.