I believe the LA Times also has some kind of demographic data in maps online somewhere showing the crime rates of the various areas of the city. Parts of NoHo can be bad and other parts near the subway can be okay. LA is fragmented - one block can be good and the next crap - so narrowing it down to specific hoods can be kind of hard.
West Adams, South Central, Watts, Boyle Heights, Crenshaw, Leimert Park, Pacoima, Sun Valley, and parts of damn near everywhere else. North Hollywood is not dangerous, Compton isn't a neighborhood, it's its own city, and most of the shitty parts of Pico and Olympic are in West Adams (i.e., Pico-Union). While Mid-City and Echo Park aren't exactly the best place to find yourself alone and drunk, they don't deserve to be considered "most dangerous," because there's a lot of decent folks mixed amongst the assholes. Hollywood doesn't even make the top twenty most dangerous neighborhoods. There's crime, sure, but to compare it to Compton? Dude, where are you from?
These places aren't uniformly horrible, either. Except, maybe, Watts. I've never seen a damn bit of good from that place.
Ok, most of Mid-city (and Pico and Olympic) really is not that bad. I'm a teenaged girl and I frequently walk around or go for runs by myself in the area and I've never had any trouble other than being whistled at from a passing car. Just don't hang around on the street by yourself after 10 pm.