I would echo much of the above info. Having grown up in Fairbanks, I encountered dozens of moose and never once had a problem. The one rule that most people seemed aware of (and took seriously) was to avoid a mother who has calves. This can be a bit tricky, since it's possible they won't be standing next to each other (although in my experience they often were). The best strategy is probably to not approach any moose, and to actively move away if you see calves. Other than that, I wouldn't be concerned if I encountered one on a trail--though their size can be daunting the first time you see one in person.

In general I'd say moose are pretty calm creatures that would just as soon leave you alone. And I'd be very surprised if one came after a person unprovoked. Our dogs would go after the moose whenever they wandered near our house, and the moose did not care for that --but nothing bad ever came of it.