It's a tale as old as time: when you're prescribed a course of antibiotics, finish it no matter if you feel better after a few doses. The implicit rationale behind that maxim was that if one is being prescribed antibiotics, it is because they have been accurately diagnosed with a bacterial infection in which antibiotic treatment will be helpful.
Every antibiotic one takes has two aspects to its nature. Antibiotics, even narrow spectrum ones, impact not only the offending bacteria but also others who are bystanders. Those bystanders are reduced in population opening up space for more dangerous bacteria as well as putting pressure on bacterial populations to select for and evolve resistance (collateral selection). Broad spectrum antibiotics do this on a larger scale and that's why they should be used only when the clinical situation warrants it (i.e. wide uncertainty about the cause of a patient's symptoms).
There is a risk benefit calculus that must occur with each dose of an antibiotic. Does the risk of antibiotic resistant bacteria developing and antibiotic side effects occurring outweigh the benefit of the antibiotic. Obviously, in a viral infection the risk strongly outweighs the benefit.
The other aspect of this issue is that often antibiotic courses, even when they are needed, are prescribed for arbitrary amounts of time. Courses of 7 days, 10 days, 14 days may have little to no rationale behind them. More and more studies are showing shorter course therapies are optimally effective and there has been a movement to shorten courses of antibiotics as much as possible. A new piece in the British Medical Journal is a tour de force as is this excellent piece by Brad Spellberg.
The point is that if an antibiotic is prescribed injudiciously -- as most are -- each unnecessary dose one takes is harmful. Also, each prolonged course of antibiotics that exceeds what is necessary confers unneeded risk. Of course, when a course is appropriately and rationally constructed to ameliorate the infection one should take the prescribed dose so as not to foster recrudescence of the infection with possibly resistant organisms (targeted selection).
Antibiotics are a precious resource that changed the face of medicine and improved human life immeasurably. The threat of antibiotic resistance is one of the most pressing problems medicine faces. Exploding arbitrary dogma to optimize antibiotic use will be essential.