Ulysses is full of that most common thing – death. Stephen Dedalus's mother has died between the end of A Portrait of the Artist as a Young Man and the opening of Ulysses, and he is tormented by feelings of remorse and guilt because he refused to pray over her before she passed. Leopold Bloom is a man who is in a sense living between two deaths – his father has committed suicide, and his son Rudy died over ten years ago, at the age of just eleven days. Thus the characters in the book are intimately aware of what a fleeting thing life is, and we are exposed to a great deal of their thoughts surrounding human mortality. At the same time, this isn't all super heavy-handed and serious. In "Hades," for example, you'll find that some of Bloom's thoughts on death are actually hilarious. Example: why don't they bury people long ways up instead of horizontal, so as to save space?
Stephen's vanity blinds him from any real sense of his own death. All he can imagine is the completion of his great artistic project, and young as he is, everything else seems tangential to it, including his own life.
In contrast to Bloom, who realizes that he is the last of his family line, most men in the novel never have to come to terms with what it means to be mortal. The other characters that speak of death seem to harbor the belief that by reproducing, they are guaranteed a form of immortality.