While Jude and Sue's romance may briefly trick you into thinking that this novel is going to be the love story, in the end, Jude the Obscure is primarily a tragedy. Thanks to Jude's tragic flaw—his obsession with Christminster and with becoming a scholar—the novel ends with shattered dreams, lost love, and dead children. It doesn't get much more tragic than that.
Still, while tragedy dominates, don't forget that Jude the Obscure also serves as social commentary. Hardy makes it very clear that he questions strict Victorian moral conventions, as well as people of the period's thoughts on marriage, religion, class, and gender. As the Sue sums up, about the conservative, hidebound people observing Jude and Sue: 'Their views of the relations of man and woman are limited' (3.6.69).
Obviously, if you start a book when a character is eleven years old and follow him until his miserable death at thirty, you are probably going to get some coming-of-age action going on. And Jude the Obscure does include some coming-of-age elements, though it also bends the formula a little bit.
Over the course of the novel, we get to see Jude both literally and symbolically go from boy to man. He gets married, finds the love of his life, gets divorced, has children, loses his children and the love of his life, gets remarried, and dies—that's quite a journey away from his childhood hopes and dreams. The one catch to this coming-of-age formula is that, even as Jude ages, he clings to many of the hopes and dreams of his youth.
His life with Arabella and Sue changes him, but not in the grand way that some coming-of-age stories portray. He loosens up on some of his religious beliefs under Sue's influence, but he clings to the dream of Christchurch almost until the bitter end. Still, before he dies, Jude admits that life has taken its toll on him and that he is different from the boy he once was:
'The theologians, the apologists, and their kin the metaphysicians, the high-handed statesmen, and others, no longer interest me. All that has been spoilt for me by the grind of stern reality!' (6.9.18).
After being refused entry into university because of his low social class, winning and losing the woman of his dreams, suffering through two marriages to the same awful person, and facing the deaths of all three of his children, we can't blame Jude for losing interest in the intellectual and spiritual stuff he used to care about so much.
By the end of the book, Jude's pleasure in religion, philosophy, and politics have all been ruined by "the grind of stern reality," in one of the grimmest versions of coming of age that we have ever come across. Clearly, if this is what it means to "come of age," sign us up for eternal childhood.