Interestingly, my only two close encounters occurred during primary flight training - never one since (knock wood!)
One was primarily a comm error, and in the airport pattern. We did a practice go-around, and noticed another Cessna at the hold line as we flew down the runway. Climbed out, turned X-wind, turned downwind, and as we rolled the 152's wing level - surprise - there was that "other" plane - also rolling onto downwind 150 ft. away at our altitude. We did a 360 away from the other plane to come back on downwind with reasonable spacing behind him. Turned out he had been on an outdated CTAF frequency, so we never heard his position calls.
In that one case, I had that "sixth-sense" hairs-on-the-back-of-the-neck feeling, due to the lack of any radio calls, and was watching for the other plane all through climbout and x-wind legs. Even said to my CFI, "I can't see that other plane anymore - did he take off?" And even so....
The other was nearby in the practice area (but not the pattern) - practicing a tight spiral descent, and suddenly we were face-to-face with a small twin in cruise 100 ft. above us - 15 seconds earlier and we'd have been in the previous turn of the spiral - at his altitude...
I live about 6 blocks from where the wreckage fell in this one:
mid-air collision of 2 private planes over the city of denver. (you can ignore the conspiracy-buff BS. The report is otherwise factually correct) It was in a VFR corridor between the foothills of the Rockies and the KDEN Class B, so heavily travelled.
My take-away is that - regardless of theory and statistics - eternal vigilance will reduce the number of near collisions overall, and reducing the number of near-collisions overall will reduce the number of near-collisions where "near" is within the wingspan of the aircraft.