On the bike trail it is crucial to do a shoulder check when changing lanes. Some people get "in the zone" and ignore all other traffic in the singular pursuit of the shortest times. They will get very very angry if you get in front of them, if they spot you at all instead of just slamming into your rear tire at full speed.

I personally can't stand to ride without a mirror for situational awareness (or, if on road, a mirror and also radar).