I arrived in Winterhold, about to join the college, when suddenly a dragon attacks. I kill it, and the townspeople turn on me: "We don't need your kind here!" Even when I run up to the college entrance, Faralda is shown hostile, I can't talk to her, and so I can't enter the college. WTF?

I tried going to an older save and starting other sidequests, but the same thing happens in every town I go to - Dragon attacks, I kill it, and NPCs turn hostile. They won't even stop after I put my weapons away. Any help would be appreciated.

You struck an NPC in combat somehow. At least in Oblivion it was 3 strikes and your out, but in Skyrim 1 hit from some splash damage from a shout or area affect spell makes the engine think you directly attacked them. It's a joke, you have to be very careful in combat when non-follower NPC's are nearby.

Just let the dragon kill them considering they are all ungrateful.

You may have hit a neutral (effectively negative faction in Skyrim) person, or it may just be because you didn't talk to Faralda to gain entrance to the College.

Let them kill the dragon, which will take a few minutes, and try to talk to Faralda again.

I had this issue with my 'zerker when he tried to go there to learn Resto/Alteration spells.

This happened to me last night outside of Riften. Minding my own business when a dragon swoops down and starts attacking the town guards. I turn and pummel the dragon with arrows from a distance. After the battle i absorb the dragon soul and loot the corpse. Then the guard comes up to me, not thanks for your help or wow you are the dragonborn or I can't believe I am still alive, just pay a bounty of 40 coins or go to jail.

Are you an Argonian?

Odds are you killed a chicken.

you definetely attacked someone you shouldn't

or do you turn dead towns people to zombies?