Bacteria, single-cell pathogens, have one huge advantage in the evolutionary game. While it takes the average human about 25 years to reproduce, bacteria can do it in minutes. So a chance change, which gives a bacterium just a tiny advantage, can rapidly spread.

The classic example of this is antibiotic resistance. Antibiotics exert enormous selective pressures. If, by chance, a mutant appears that can tolerate an antibiotic, it is at a huge advantage.

Now, because of our lax use of antibiotics, resistant microbes are a big problem. Use of antibiotics when they are not needed (e.g. for viral infections) and in agriculture (they are widely used as animal growth promoters), and a tendency for people not to stick to dosages prescribed, creates a situation where low levels of drug exist. Partially resistant bacteria have a survival advantage and spread. Now, MRSA, multidrug-resistant TB and other drug-resistant bacteria are a major threat worldwide.
Hijacking the cell

Viruses, tiny particles that infect and take over a cell, also have numbers on their side. A single infected cell can spew out millions of new virus particles. Once again it is diversity that underpins their success. In most organisms, heritable material such as DNA is copied extremely carefully. In many viruses, though, genome copying is extraordinarily haphazard. But with millions of copies produced in each cell, plenty will be fine – and among the millions of 'defective' ones there may be some promoting drug resistance.

This is one reason why HIV is so dangerous and flu is so difficult to treat. They are moving targets: no sooner has the immune system learned to recognise one form than it has changed into something else.
Mixing pots

Virus genomes can also swap bits of their genome with one another. This may create defective viruses, but occasionally something with brand new powers can arise. This is probably how the Spanish flu epidemic of 1918 began. An avian flu virus mixed with a human flu virus, possibly in a pig (pigs can be infected by both avian and human strains of flu). This new virus could infect and be spread between people, and was lethal.

This could happen again, with avian flu strain H5N1. Currently, this strain can be spread from birds to people but not between people. But if it swaps genes with another virus and becomes transmissible between people, the potential for a global pandemic is very real.

I don't go to mythical places with strange men.
-- Douglas Adams, The Long Dark Tea-Time of the Soul.