Most vehicles' oxygen sensors can be checked for inconsistent performance with a scan tool or lab scope. Vehicles that are run off road in muddy conditions may notice a shortened oxygen sensor life. The sensor has to be able to read the outside oxygen and if it's covered in any way the sensor won't read properly.
0xygen sensors provide information about the fuel mixture. The PCM (Powertrain Control Module) uses this feedback to constantly re-adjust and fine tune the air/fuel ratio. This keeps emissions and fuel consumption to a minimum. A bad oxygen sensor will typically make an engine run rich, use more fuel and pollute. Oxygen sensors deteriorate with age and may be contaminated if the engine burns oil or develops a coolant leak.
OBDII vehicles have several oxygen sensors. You'll typically find one in each exhaust manifold (so on a "V" engine you'll often find two). You'll also find another "downstream" oxygen sensor behind the catalytic converter to monitor converter efficiency.