I visit the doctor if a problem persists over time, or if there seem to be complications, but otherwise I let minor injuries and illnesses progress on their own terms. It's an attitude I share with most of my family; we generally use our own judgement as to whether a problem warrants medical attention. Perhaps that isn't the wisest approach - after all, I'm sure the doctor is a better judge of these things than we are

- but we don't like making appointments over non-recurring ailments that can be overcome without help (don't want to congest the system, you see). A minor virus or a sprain doesn't require attention, but if it hasn't improved within a period that I judge should have been sufficient, or if it gets worse/acquires additional problems, then I consult the doctor for advice. Basically, I go to the doctor whenever I'm unsatisfied with my health, but I make allowances for the fact that you're never going to be in
perfect health, and that your own judgement has to play a role in these things lest you push back appointments for those who have genuine issues.
That said, my family and I rarely have accidents or such; if we did, then we'd probably book an appointment for a checkup, so as to be on the safe side. I also like seeing the doctor for a general checkup once a year or so - that doesn't take up much time and lets them catch any potential major or long-term problems before they become dangerous; the doctor can see the potential warning signs and recommend lifestyle changes or further checkups as (s)he decides is wise.
All that said, I have to admit I wasn't necessarily very smart about seeing doctors in the past. I was so used to having aches and pains, and a general heavy fatigue, that I dismissed most new pains as "part of the way my body works". And after all, my checkups always found me in great physical health - blood pressure, heart rate, blood chemistry, etc, all normal - so I was able to dismiss my physical problems. I must say I wouldn't recommend that now - I feel I failed to take advantage of what was available to me out of a misplaced sense of intrusion. It was only comparatively recently that it occured to me that constant pain and fatigue is probably a problem in its own right, that I have a medical service there for me, and that it's not irresponsible to try and get to the bottom of problems of this magnitude.