My first general observation is that you should always be observant, no matter where you are. Who is behind you, what dark corners lie ahead, where is the nearest exit. These don't require a ridiculous level of security and paranoia (i.e. a US airport post-9/11) but just a general ability to observe your surroundings and know your options. Glances and observations, that's all. Don't walk around with your head in the clouds. I generally feel that with that basic level of situational awareness, you'll avoid 99% of the problems you would encounter in almost any place on Earth.
My second observation is that Hong Kong 'feels' very safe. I don't know if it is the number of people around, or the basic general rule that expats are ignored (hey, whatever happened to that guy that got sliced up at the Rugby 7s last year--that was the last major triad attack on a gwailo I think). Basically, you will not get the 'creeps' as much as say walking through the back alleys of Manhattan at night.
Of course, I'm a big white dude in a black leather coat and Terminator shades who scares people when I walk and generates concerned stares from cops who think I'm with the Russian mafia they've heard about on tv, so your mileage may vary.