The most prominent is antibiotic resistance. Drug resistance is also found in some tumor cells, which makes it more difficult to use chemotherapy to attack tumors made of those cells. Resistance to antiviral drugs also occurs in virus populations, notably HIV. When a drug is administered, those organisms which have a genetic resistance to the drug will survive and reproduce, and the new population will be drug-resistant (see natural selection, selection pressure).
In the presence of drugs, pathogens have evolved sophisticated mechanisms to inactivate these compounds (e.g. by pumping out compounds, mutating residues required for the compound to bind, etc.), and they do so at a rate that far exceeds the pace of new development of drugs. Examples include drug resistant strains of Staphylococcus aureus, Klebsiella pneumonia, and Pseudomonas aeruginosa, and Mycobacterium tuberculosis (TB) among bacterium and HIV-1 among viruses. Indeed, no new antibiotics have been developed against TB in thirty years. Efforts to develop new antibiotics by the pharmaceutical industry by large-scale screens of chemical libraries which inhibit bacterial growth have largely failed, and new tetracycline and sulfanilamide analogs will likely engender resistance and will quickly be rendered useless. The resistance problem is compounded further by indiscriminate and inappropriate use of antibiotics and anti-viral compounds without compliance measures or public health policies to reduce disease burden. Finally, with current legislative restrictions, the very high costs associated with clinical trials (e.g. ~$400M to bring new tetracyclines to market for an expected revenue of ~$100M), the failure to control generic sales, and the capacity to generate substantial revenues from medications for chronic illnesses, there is little if any financial incentive for big pharmaceutical companies to even develop new antibiotics, and small biotech companies simply do not have the resources. The search for novel anti-viral compounds has been somewhat more successful and largely motivated by the AIDS epidemic, but drugs have been developed principally against viral targets, and mutation rates among viruses still outpaces new development. One positive development has been vaccines, which are promising for some bacterial and viral illnesses. But vaccines are not successful in all cases (e.g. in young children), and adequate resources have not been made available.
Drug resistance has a high metabolic price, in pathogens for which this concept is relevant (bacteria, endoparasites, and tumor cells.) In viruses, an equivalent "cost" is genomic complexity.