What is an example of when a limit does not exist?

For example, ${\lim}_{x \rightarrow 0} \frac{1}{x}$ DNE because ${\lim}_{x \rightarrow {0}^{-}} \frac{1}{x} = - \infty$ is not equal to ${\lim}_{x \rightarrow {0}^{+}} \frac{1}{x} = + \infty$.