My students get tired of hearing me say this over and over, but it's TRUE - reading your own work out loud is crucial. Whether you're writing an essay about Othello, a poem, a novel, even an important email. There's something about hearing your own words that brings them to life in a different way. And - an even better reason - you'll hear things like missing words, choppiness, and unnatural dialogue that you wouldn't otherwise recognize. If you stumble over a sentence or phrase, you'll know that particular section should be re-worded, clarified, tightened.
Esther Freud states it well: A story needs rhythm. Read it aloud to yourself. If it doesn't spin a bit of magic, it's missing something.
So, there's yet another good reason - even prose should have a sort of rhythm to it, a natural ebb and flow. And reading your work aloud will help you to hear that rhythm (or the lack of it).