I'm going to contribute my two cents to this conversation. I have personally been accosted several times here, and have known several people (both locals and foreigners) who have been beaten/mugged. Thankfully it is mostly petty crime, and that there isn't a big gun/gang culture, or one of hard drugs. I know that they have paco here, but at least they don't have crystal meth or a slew of other hard drugs. Hopefully those don't make their way in.
When I moved here in '06 I started out in Recoleta (a safe, common choice for a newbie in the city). Prior to starting an internship here I went to Mataderos to scope out the internship location in the early afternoon. Not two minutes off the bus my partner and I got jumped by a couple of thugs with knives in their pants coming from a villa. We were able to fight them off and run to a nearby copshop. The stationed cop was perplexed and asked us what in the world we were doing out there. Chalk that one up to a shitty company who would send a girl out there by herself everyday. Needless to say I asked for a reassignment. I got placed in Boca, and never had an issue there, but also never wandered around with anything but papers in my hands according to the
express warnings of the women who ran the defensoria. I did get to tour the "do not enter" parts of Boca with one of the therapists, and see where the child prostutition and other unseemly things happen there. Also in La Boca when visiting a friend, I stopped in a kiosk and the owner told me to leave the area, as I was not going to be safe there (it was near dark). After I returned from a month in Santiago (no muggings or any problems there) I moved to San Telmo. Shortly after moving in someone (a well dressed 'gentleman') entered our building, got into the elevator with a tenant and pulled a gun on her, then robbed her apartment. Nobody else in the building was affected.
One evening I was coming home from my internship (I carried a backpack with workout clothes, books, etc.) and we got motochorro'd (or however you'd use that as a verb)--held up at gunpoint by two women. I handed over my backpack when the woman cocked the gun. Whether the gun was real or not wasn't something I was interested in finding out. It was early evening in San Telmo on a busy street with streetlights, etc. Nobody did anything to help, and only once the women were back on the moto and gone did anybody approach us to offer help or condolances.
So, feeling unsafe, we moved to Cañitas. There nothing happened to us directly, but we did witness a couple of occurrences with someone running with a stolen bag, or a woman crying in the street after being robbed. After six or so months we moved to Almagro where we lived for a couple of years, and our flatmate was robbed by the maid. I had two bikes stolen (from the street) while living there, and heard about some local cafés and restaurants being held up by groups of thugs with guns. Once had someone try to grab my bag from me while walking home (a few blocks away from my apartment) after a dinner out. Having gotten better at fighting off street criminals I kicked him in the crotch, my boy hit him in the head, and he gave up and ran away leaving me with a purse with a broken strap. I was pretty proud that I had the presence of mind to yell after him, "puta de mierda", but every time anything happens to me is an experience that left me shaken.
We now live in Caballito (casi Flores) for over a year, and haven't had anything happen to us out here, but that's not to say we haven't been in areas around here where we turned around and headed to somewhere with a safer vibe, or felt the need to leave a certain area before dark. Once while I was riding my bike to work I saw an old woman crying with a bleeding face talking to the police , she had clearly had been recently mugged (it was 9 in the morning). I've explored the vast majority of Capital and beyond (usually by bike), and for the most part haven't had problems. If I pass a group of potentially suspect people, I don't speak (especially not English). We also now carry pepper spray and a billy club--just in case. Thankfully we've never had to use either.
As many people have pointed out, sometimes it's the luck of the draw, sometimes someone is in the wrong place at the wrong time, sometimes they're doing something stupid, but sometimes there's nothing that you could have done to help or stop it. Operate with the best possible information available to you at the moment, keep your eyes open, and trust your gut instincts and you'll probably be just fine. I'm certainly not saying that this is the most dangerous city, as the definition of "danger" is particularly relevant to your personal experience and ability to cope. That said, Buenos Aires is definitely a city where you have got to watch your back. It's always a good idea to have cab fare in your pocket in the event that you need a quick escape.
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ETA: Oh I almost forgot. We had a fire in our apartment in Almagro due to faulty electronics/wiring. The FIREMEN tried to steal every last belonging of value from us (including rifling through our drawers looking for hidden cash). Thankfully we arrived in time to stop them from stealing our stuff--but unfortunately didn't stop them from being pissed that they didn't score the loot and spreading vindictive rumors about us and our careless ways of starting fires (something about unattended burning candles on the floor during the day in the middle of summer--wtf) and endangering the whole neighborhood. After that experience I got the consensus that oh yeah, you must hide valuables and be careful when letting the police or fire fighters into your home. Great.