The Odyssey of Homer is one of the greatest works of western literature. There are many ways in which it has helped to shape the western canon. However, the primary way in which it has influenced western literature is through the theme of homecoming and the idea of a journey.
We can see this as early as the great work of Virgil. In the opening lines of the Aeneid, we see this theme very prominently. The first few words are a quotation from Homer's Iliad and Odyssey, and more importantly the work chronicles the journey of Aeneas. The first few lines read:
"Arma virumque cano, Troiae qui primus ab oris
Italiam, fato profugus, Laviniaque venit
litora, multum ille et terris iactatus et alto
vi superum saevae memorem Iunonis ob iram;"
We also see this them in later works as well. For example, one of the most famous works in the Medieval ages was the Journey of St. Brenden. More recently, we see that the Odyssey has influenced James Joyce (Ulysses) and Ezra Pound (Cantos), to name a few. In fact, any work of a journey can be traced back to Homer's Odyssey.