Biggest advice: what may seem cheap to you may be expensive here. Especially notebook computers, iphones, ipads, ipods, ebooks. Do not use them in public, I´ve heard even of thieves entering a cafe at gunpoint to rob computers! Do not use them on the subte (subway), or in plazas. If you do, don´t leave a computer unattended, even for a minute to go to the bathroom.
Be very careful taking photos or video in public, never go alone.
Do not use jewelery that looks expensive or is expensive, especially watches.
I still use an old cell phone and my husband has the cheapest smart phone on the market, in part because he doesn´t want to be a target for robberies.
I have lived here for ten years, and I have been pickpocketed 5 times, 3 times were really my own fault for putting my money in the back of my backpack, etc. I was also robbed twice in Barcelona in a week, and I lived in NY for four years and never robbed there.
People here like to exagerate and complain, take it with a grain of salt. Crime has gone up compared to 50 years ago, and that is how most locals judge the situation. There is a lot of robbery, but very little "serial killer/mass shooting" crap compared to the US or even Brazil or Mexico.
You are proabably safest in areas with a lot of people on the streets, and less safe in empty areas, even if they are "nice".