Stochastic differential equations. Originally invented in order to describe Brownian motion. Langevin equations are similar to normal differential equations, but contain a 'noise' term intended to describe some unmodelled aspect of the system, for example a random force, an unknown external force, or, as with Brownian motion, another part of the system which contains too many degrees of freedom to be able to model.
Since these equations generally contain some random element, a deterministic solution cannot be found, and the solution is generally in the form of a probability distribution.
Examples occur in fluid dynamics, lasers, and population dynamics to name but a few.