A central problem is that you get loads of false positives when you are screening symptom-free individuals, and these false positives can cause real harm: beyond anxiety, they often bring on potentially painful, expensive and side-effect causing treatments. Just see the recent recommendations over the PSA test: http://en.wikipedia.org/wiki/Prostate_cancer_screening.
Definitely go to the doctor if you notice any symptoms or worrisome changes. For other types of screenings, be aware that the recommendations often change and that there is a real cost/benefit analysis (even in terms of your own body, not just financial cost) to be done.
