I go to a primary care practice which has 6 doctors, each with their own assistant, and nurse practitioners too. If I call today, usually they can see me same day or at latest, the next. There's always someone available, and if my own doctor is out, another wil cover. And the NP's can handle a lot of the basic stuff, like giving shots or checking out that rash... I've seen NP's atleast as often as I have the Dr., and the quality of care was no less. It's the best-run practice I've ever been to.
I also see a counselor and a psychiatrist at a clinic that can always be there when you really need them. If it's the dr.'s day off, the nurses will get a hold of him, and there is a crisis line and respite 24/7, so you're never stuck w/o help and it integrates seamlessly with your regular care. Very well-managed.
But, still, people should use common sense and courtesy, save the last-minute appointments for when it's urgent/sick visits, and schedule the routine visits in advance and remember them, write them on the calendar, keep a date book, whatever it takes. I am the most disorganized person I know, but since I started carrying a little datebook with me at all times, and all appt.s go directly in it, I have missed only a couple (since I missed my bus; I did remember, though).