Density lambda e^(-lambda x), mean 1/lambda, standard deviation also 1/lambda.
It is the waiting time between Poisson events, and the continuous analogue of the geometric.
Memoryless, and the only continuous distribution that is: P(X > s+t | X > s) = P(X > t). A component that has survived ten years is as good as new under this model, which is exactly why it is often the wrong model for physical wear.
Useful fact. The minimum of independent exponentials is exponential with the summed rate - so competing risks combine trivially.