In circuits, the voltage and current can be measured by the use of voltmeters and ammeters, respectively. However, the placement of these devices into the current alter the actual voltages and currents of these circuits. This is why voltmeters are very high in resistance and wired in parallel, and ammeters are very low in resistance and wired in series. This is to minimize the essential error or alteration they are causing, and since there is really no "zero" or "infinite" resistance, these errors will just have to be diminished by improving technology, though obviously we have come very far in this respect.
There are other examples, such as measuring temperature with a thermometer. The thermometer slightly changes the temperature of the liquid it is placed in. Also, electrons are detected by using photons, and this interaction alters the path of the electron.
This is often confused with Heisenberg's uncertainty principle in quantum physics, so I'll mention that briefly. Basically, the precision of a pair of physical properties of a particle (complementary variables) can be expressed as an inequality.
Here, x and p are position and momentum. As the precision of one gets higher, the precision of the other gets lower, and this relationship can be expressed as a fundamental limit using inequalities.