I actually just graduated with a degree in classical languages. Did Greek, Latin, and a little classical Hebrew just for kicks. In Greek I very much enjoyed reading Xenophon. The Odyssey is probably more fun (and easier) to read that the Iliad, unless you want to know 500 words for "stabbed in the spleen." In Latin, I very much enjoyed Livy's 'Ab Urbe Condita" as well as the poems of Catullus (though the latter can be quite racy at times...okay, most of the time).
@abgemacht - Lots of people who get classics degrees go on to (1) seminary, since many Christian documents are written in Greek/Latin, (2) law school, since many of the best works on rhetoric are written in Latin, (3) med school, since most medical terminology comes from either Greek or Latin. Really this just scratches the surface though. I've got a friend who got a degree in classics and then got a job in computer programming (with little to no prior computer experience). She said in her interview "I can learn Greek and Latin, I can learn your programming language." They agreed and hired her.
Studying classics is not just about the languages and the cultures (though that's what draws most classics students to the programs). It's about learning critical thinking on a scale not often reached in any other discipline (in my humble opinion).