It's always a good idea to read your stories aloud. I know many people who do it. For years, I read every word I wrote to my husband (bless him!) on a nightly basis. I still read aloud to him occasionally (though kids and life make a nightly session impossible), and I've practiced for readings with him, too.
To my mind, reading aloud is an important test for any story - and it works on several levels.
The first thing that reading aloud can do is give you some distance on what you've written. Sometimes you spend so much time going over and over the words on the screen that you know them by heart, and you stop being able to see problems that might be there. Reading aloud is one way to push that text away, and put it into a context where you can be more aware of what's actually there, rather than what you think/know is there from the million times you've run your eyes over it. Printing out the story and looking at it that way can have a similar effect, but does require more paper and ink!
The second thing that reading aloud can do for you is give you a sense of the rhythmic feel of your prose. As you go through, awkward spots will give you pause, or even cause your tongue to stumble. When this happens, it's a good idea to change what you've written - because if it makes you pause or stumble, chances are your readers will have the same problem.
Those two aspects of reading aloud are helpful from the very beginning of the writing process. Once you've gotten a bit further in, you may be interested in designing character voices - and reading aloud can help you here, too.
If you've never had the experience of "reading in voices," I encourage you to try it - either with your own work or with the stories of others. You don't need to alter your voice in any extreme way; nobody needs to morph into Frank Oz to experience how this can help. Put yourself into the character's mindset as you do when writing his/her point of view, and see how your voice comes out. A strong character voice will give a distinct feel to the sound of your reading.
This can help you in two ways. First, if your writing is falling out of the voice into a more generic mode, you'll hear it. The sensation of that voice will change and you'll start sounding more like a generic narrator. Second, you should notice that your voice needs to change when you change points of view. If this doesn't happen, it's a red flag that maybe the voices aren't distinct enough. I actually surprised myself when I practiced reading The Eminence's Match aloud, and I stumbled when I first changed scenes. Suddenly I wasn't in Nekantor's voice any more, I was in Household Director Samira's - and I had to stop and think through what she should sound like when I read. That prepared me for how I might have to change my reading voice again when I hit another character point of view. Fortunately, the voice differences were already present in the manuscript (I just hadn't read it aloud in quite a while!). It was really fun to think about what to do with my reading tone in the various scenes, and the reading at BayCon turned out to be gleeful fun for me.
In any case, it's always a good idea to read your work aloud. You can learn a lot about it (and about reading it to others, a useful skill), and even help to push your work to the next level in revisions.
It's something to think about.