Traveling for a long time alone for the first time saddles you up with a lot of unanswered questions. More often than not you're surrounded by people who have no experience traveling alone and their comments do not help much to build up confidence for the upcoming adventure.
That being said, both Central and South America have their fame of being 'dangerous'. Is this true, Yes, I've seen some troubling things happening on the streets but these also happen in big cities in the States or Europe.
I backpacked 18 months, traveled thousands of kilometers, cities, jungle, islands, mountains, carnival, spent 6 weeks in a street child care center in the favelas of Salvador da Bahía (Brazil)... nothing. I repeat, nothing happened.
Use common sense. Avoid badly lit streets at night and if your sixth sense is giving you the "something's wrong" sign then take a taxi to your destination. Lock your backpack while traveling on public transport and in dorm rooms, don't walk the streets with valuables, always have some cash on you ($10) in case your 'worst case scenario' comes true, they just want money. Never argue or start a fight, it's just money.
I met a lot of young backpackers on the road. They were all having lots of fun.
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Backpacking in South America