I avoid taking any medicines unless really necessary (i.e. can't function without it and need to), which includes ibuprofin, cold medicine, etc. I'm not uber paranoid about it (I don't think :-)) but I think that people take medicines way too much/easily. I haven't had antibiotics in maybe 15 years. Like you I'm lucky to get sick very infrequently.
When I do, I just make it a point to sleep as much as possible, if I'm in really bad shape I'll take Nyquil or something to put me out (though that seems to be getting less effective on me as I get older). I got the stomach flu a couple of months ago and, once I was done praying to the porcelin, I just drank a lot of fluids including drinks made from fresh ginger, gradually re-hydrated myself and slept a lot.
Fasting is often not a bad idea, not intentionally restricting your food if you are sick and hungry, but the "feed a cold" mantra is often not a good idea. Your body can easily live for several days without food, and relieving it from the burden of digesting can give it more resources to fight off an illness.
Not to get all hippy, but being sick is something that just happens sometimes, and your body has its ways of fighting it off, and piling on various medications in an attempt to hide the symptoms or make your body artificially more or less active may just compound the problem and make your body fight off more than one thing at once.
My daughter (age 6) has occasional ear aches, and we found that 2-3 drops of warm (not hot) olive oil in the ear canal clears it up every time. I know that if we take her to the doctor, they'll barely even look at her before prescribing 10 days of antibiotics. The olive oil takes literally less than 5 minutes.
I think it is a good idea to resist the knee-jerk Western trend of reaching for a pill every time the slightest thing goes wrong. That said, when you're really sick, go to the doctor, don't go all Scientologist and try to treat some life-threatening condition with a positive attitude.