Recurrence entropy (S) is a novel time series quantifier based on recurrence microstates. Here we show for the first time that max(S) can be used as a parameter-free quantifier of short and long-term memories (time-correlations) of stochastic and chaotic signals. max(S) can also evaluate properties of the distribution function of the data set that are not related to time correlation. To illustrate this fact, we show that even shuffled versions of distinct time correlated stochastic signals lead to different, but coherently varying, values of max(S) . Such a property of max(S) is associated to its ability to quantify in how many ways distinct short recurrence sequences can be found in time series. Applied to a deterministic dissipative system, the method brings evidence about the attractor properties and the degree of chaoticity. We conclude that the development of a new parameter-free quantifier of stochastic and chaotic time series can open new perspectives to stochastic data and deterministic time series analyses and may find applications in many areas of science.