Even after all these years, I'm still struck by the fact that Taipei was relatively crime-free. I don't recall ever being concerned about getting attacked or robbed while I was there back in 1973-1974. If such things ever happened, I never heard about them. I felt perfectly safe walking along the street in downtown Taipei at any hour of the day or night. Apparently, it's still like that today, according to the US State Department.
That's not to say there was no crime. Home burglaries, for example, were always a possibility. I hired a houseboy at the hostel, mostly to keep an eye on things. He definitely earned my trust the time I inadvertently left a fair amount of cash on the table in my room one morning. Not only was it still there when I returned home that night, but he had neatly sorted and stacked it for me.
During my tour I "house sat" a few times for some of the Navy officers at TDC who wandered off to Hong Kong or somewhere on vacation. I think they had full-time neighborhood security guys who roamed up and down the block from time to time. Even so, they felt a little more secure having someone in the house every night as well. It gave me a change of scenery for a few days and usually resulted in a good meal at a nice restaurant when they returned -- a definite win-win situation.
I'm now retired and live close to a major university in the Midwest. We don't have a horrific crime rate here, but I wouldn't even consider going for a walk downtown at three o'clock in the morning. In Taipei, a city of close to two million people at the time, I wouldn't have hesitated.