The Odyssey is the classic hero's journey, both for Odysseus and for his son Telemachus. If you can identify how they both go through the hero's journey, it is pretty simple to find other examples of heroes, both modern and classic. To get you started, think about the first phase of the hero's journey. This is where the character is in his or her own world, going about his/her business as usual. Maybe they're bored, maybe they're content. And then there is the call to adventure. If you like movies, an easy one to use would be The Hobbit. We have Bilbo Baggins, an ordinary hobbit, going about his mundane life. His only concern is keeping his hobbit hole tidy and having enough to eat. Then along comes Gandalf, followed shortly by a dozen dwarves, and their main goal is to drag him out on an adventure. He resists -- because that's what heroes do in the beginning. Odysseus does the same thing. He wants to stay home with his wife Penelope and his newborn son Telemachus, and so he pretends to go mad so he won't be asked to go to Troy.
Hero's Journey information is all over the Internet, and your best bet for parallels is to find a book or film you know well, and line up all the stages of the journey with it. Tons of movies and books have really clear examples, but a few are: Jaws, The Lord of the Rings, the Harry Potter series, the Star Wars films (the original ones), and Kung Fu Panda.