This wiki page says
A continuous probability distribution is a probability distribution with a cumulative distribution function that is absolutely continuous. Equivalently, it is a probability distribution on the real numbers that is absolutely continuous with respect to Lebesgue measure. Such distributions can be represented by their probability density functions. If the distribution of X is continuous, then X is called a continuous random variable. There are many examples of continuous probability distributions: normal, uniform, chi-squared, and others.
It seems that the first sentence in the quotation implies that there exists some other types of probability distribution that could not be associated with a cumulative distribution function?
Is my understanding right, or I am over reading the part?