I was quite interested in this topic a few years ago. Though i can't remember why, it all started with me looking for the equation which would yield randomness as its result. Lets just say i came out dissatisfied with the result.
But regarding the topic at hand, randomness is, according to Wikipedia, a "lack of pattern or predictability in events". By scrutinizing this sentence, it becomes apparent that randomness has to do with the subject rather than the object. As in, the being or object perceiving the randomness can't understand the "why" nor the "how" of the event, but the event itself has clearly undergone a process to be what it is at the moment of its interaction with the observer. As such, any person might perceive any number of odd things during a lifetime, some of which the person's brain will catalog as "random". Thus, from this point of view, you could say that there are, indeed, several random things in the Universe.
But doesn't it feels wrong? The fact that randomness has to do with a person's lack of creativity rather than its entropy? [entropy: lack of order or predictability; gradual decline into disorder.] A quick look at math brings to mind RNG's, or Random Number Generators, which, once again, Wikipedia has a nice article about. After reading it, we can conclude that even if randomness might be attained in a closed universe, an external observer can trace the "randomness" back to its root, thus understanding it (and denying it as a true random value) which would give us the answer that no, nothing can be absolutely random.
Anybody willing to choose one argument over the other?