Yes. A typical technician working on a PCB can generate thousands of volts. SMOS logic devices can be damaged with 250-3000 volts, EPROM devices down to 100 volts, and microprocessor chips as low as 10 volts. Damage can shut down functions or create intermittent problems, and it can either be catastrophic (immediate) or latent (later as in "field failure"). (source: Phil Storrs PC Hardware Book)
Electrons are constantly being exchanged as objects interact with each other. Problems occur when the materials involved don’t allow the electrons to flow easily and reach equilibrium. Called insulators, they tend to collect electrons, which create negatively charged hot-spots on their surface.
When these charged hot-spots come in close proximity (but not even direct contact) with another object, a sudden exchange or "discharge" can occur, where electrons are suddenly exchanged to create equilibrium. That event is called "electrostatic discharge", or "ESD".
Electrostatic discharge happens all the time, especially in dry climates and in the winter season, when there isn’t moisture in the air to help bleed off excess electrons (water is conductive, so allows the electrons to flow more readily). Normally it is nothing more than an irritation, but with sensitive electronics, it can lead to PCB failures.
Wearing a grounded wrist strap and working on a grounded ESD-safe mat is the best way to prevent ESD. A wrist strap has a conductive surface that touches the skin, so can bleed off excess electrons. An ESD-safe mat works by a similar principal, so bleeds off a charge from anything on its surface. If working on a PC, you can clip the wrist strap directly to an unpainted area of the case.
Grounded wrist strap bleeds off excess electrons to prevent damaging static discharge.