Great thread! I'm 37 years old and have been to 125 countries and territories so far, plus of course numerous towns and cities. I've only ever had "something bad" happen to me twice, and both times were somewhere I considered (at the time) safe:

Brussels, Belgium: My own fault really. 30 hours of travelling from the Cook Islands and I was feeling pretty zonked out waiting for a connecting train at Brussels-North station. Someone asked me a question about the next train, and being the helpful soul I am, I assisted, only for an accomplice to make off with my rucksack in the 10 seconds I had my hand off it. It could have been worse though, I guess. While in the police office, another chap came in bleeding and crying, after being robbed at knifepoint on a train.

Montevideo, Uruguay: I'm not a naive traveller by any means, but I was reassured by various blogs and articles suggesting Uruguay is one of the safest South American countries. I'd been out drinking the previous night and taken in a wonderful cultural show which, as I found out later, was in the Barrio Sur estate, the one place tourists are advised NOT to go. But I walked back to my hotel at 2am with no problems. The next afternoon, having a pleasant stroll around the Rambla, I spotted a dodgy looking teenager making the effort to cross the busy road to approach me. First it was hand out and "money, money", but soon turned into touching, and I then spotted he had a knife. Thankfully, I could run faster than him, and was helped by a smartly dressed businessman as I panted to a stop up the hill towards the city centre. That freaked me out and I pretty much stayed in my hotel the rest of my stay.

Places I'd read about as being thoroughly dubious, and thus I remained on my guard the entire time, but nothing bad happened at all:

Rio: Took a taxi from the airport to Copacabana despite my usual "public transport only" rule. Took the bus back. Was nervous and looking at everyone like they'd be a threat the entire time I was there, but apart from lots of groups hanging around staring, everything was OK.
Manila: Was actually quite good fun in the end!
St Vincent and the Grenadines: Not much to do, but didn't feel threatened at all.
Jakarta: The biggest danger ended up being the traffic.
Albania: No problems at all, and the people were lovely.

I've never felt unsafe anywhere in the US, despite not being a driver and always walking / taking public transport. I'm good at recognising where neighbourhoods move from being nice to less nice though.

I do find though, increasingly, and especially as I get older, I'm letting bad reviews of cities on the basis of safety affect my decision to visit or not. South Africa, for example, seems wonderful, but I have this fear I'll be mugged at gunpoint within 10 minutes of leaving the airport.

I've never felt unsafe in London (though I do live here), and the drinking culture is all part of the fun here! Unless you're actively looking for trouble, or out in dodgy suburbs like Peckham or Harlesden, you generally won't have a problem.