One of the funniest things that happened to me was this:
I noticed the high elf guards marching a prisoner right outside of Whiterun, near one of the local farmhouses. I'd opted to simply leave them alone, when out of nowhere a dragon attacked. My companion (who was the early wizard character) and I immediately attacked said dragon, and my shout blew it into one of the guards, smashing him up against a wall and killing him. The rest of the guards attacked me, and I defended myself and then proceeded to loot their corpses, because why the fuck not? Well, I was pretty close to being overburdened so I fast traveled to Whiterun, and that was my mistake.
Rather than give me the chance to pay my fine they attacked. Now I ran through the town, trying to get away from them, and not attacking anyone - but my little companion had other ideas, and he proceeded to chain lightning the shit out of everyone that saw fit to pursue me with a sword drawn. Needless to say it did not end well for them, and the entire town was littered with dead guards (including two that chased me into my home) and people going, "Oh my! What happened?" every time I went back there. I have since learned not to fast travel with a fine due.