If you send out stories to magazines you'll almost certainly get some rejections. You won't like them, nobody does, but you can get used to them and accept them as simply part of the process, rather than a series of crushing blows. If it's any consolation although I've had hundreds of stories published I too get some rejections.
This is what a rejection means –
That particular story wasn't right for that particular magazine at the time you submitted it.
What a rejection doesn't mean –
You are a rubbish writer.
The story is rubbish.
You won't ever be accepted by that magazine.
I'm not saying you're a great writer, or that your story was good; unless I've read it I can't possibly tell. I'm just pointing out that a standard rejection letter means only that the particular story wasn't right for that particular magazine at the time you submitted it.
Here is some information on rejections from The People's Friend. Although some things will apply to all markets, remember that different magazines have different requirements. What doesn't suit one might be just right for another.
Stories may be rejected because they're the wrong length for the publication, or the wrong style/genre/subject. They may be seasonal and have arrived too late. Perhaps the magazine already have enough stories of that length, or genre, or even enough of all kinds of story for now. Maybe they've recently accepted something similar in style, or with a theme or location in common.
If you receive a personal rejection, or any feedback on your work, especially if there's anything positive in it, or an invitation to submit further work, then you should be encouraged. Editors are far too busy to do this for everyone, so will only spend the time if your work shows real promise.
Have you received any rejections lately? What reasons have you been given for a piece being rejected? Any tips for geting over the sting of rejection?