Unlike other punk genres, hardcore punk tends not to be associated with dress styles such as safety pins, spikes, patches etc. The musicians (and therefore their fans) follow a more dressed-down style: jeans, tees and crewcuts. Another interesting difference in hardcore punk is that it's often described as having it's own unique form.
The aforementioned Minor Threat are a famous hardcore band, though they only stayed together for three years. Despite this, however, it had a huge impact upon the genre. They strongly influenced the straight edge subculture along with a DIY view towards music distribution and concert promotion.
Another band that is linked to this DIY theme is Black Flag, who disbanded in 1986 but are still well-known within the genre. Their songs generally had strong non-conformist and anti-authoritarian messages.
Warning- these songs may contain swearing :P
Damaged- Black Flag
Straight Edge- Minor Threat