They all relentlessly chase after me. The conversation box automatically opens when they're in the vicinity. Hard to get away from. Grrr.

This happen to anyone else?

I've heard of bugs like this(everyone from a group/faction attacking you) happening, I haven't had it happen, and hope it doesn't.

They charge me like they're about to attack... but don't (thankfully). I thought maybe re-installing the game data would do the trick, but nothing.

Are these any companions in particular, or all of them?

Do you have a bounty? Several of them are flagged as being part of the guard faction, but they don't have the arrest-related dialogue, so you just get a normal dialogue window.

Farkas did this for me for a little while on my mage, which was odd because I'd never interacted with him previously on that character. He stopped after I left Whiterun though.

All of them. They even found me in the wild.

Hmmm. I don't believe so. Let me check...

had the same glitch does not come up in your crimes and stuff,so jst go up to a whiterun guard and pick his pocket or smack him to get arrested.then jst pay your fine and glitch is gone

Thanks!

Happened to me too on one of their Radiant Quests when Vilkas was my follower. He got killed, and when I returned to Jorrvaskr everyone there drew their weapons and started hacking away at me.
I exited/re-entered but same thing. Since I was married to Aela at the time, she wasn't hostile, but she also wouldn't give me another quest, saying instead "You need to finish your quest with Vilkas first."
I was at level 28 in my first playthrough of Skyrim. I didn't know about the fix that didjamom posted above, so I started a new game.