My reputation for NCR has become antipathy, but I can't remember doing anything bad. Well, except once I tried stealing from a mutant in the bar one time
and dying immediately afterward. But I think the next time I was in town, I wasn't in antipathy. The only other thing I can think of that may lower my rep is that I accidentally stood in entrances to the brahmin pins for a while, but never long enough for a guard to attack.
I've just made a character recently and here are about all the other things I remember doing so far:
-Shoveling
-Doing the quests for picking up cigs and giving someone money the bartender chick owed
-Dying a couple times in random encounters >.<
-The only thing I killed so far was ONE radscorpion
-Shopping at the dwarf's gun shop
Those are the most important things to note that I've done I think, any small things I might have overlooked?