"Get a thick skin. Every academic has piles and piles of rejection letters."
I've written about the importance of submiting work to journals before. Today, Fabio lays down the rules for graduate students who might be thinking about putting off writing that journal article until they have finished their dissertation. Don't do it; start submitting work to top journals as soon as you can. Always think about your results in terms of their suitability for publication in the journals that define your field.
The best way to do that is to make the rejection letters from top journals a part of your formative experience as a PhD student. "Get a thick skin," is exactly right. But don't develop calluses—don't get callous. You want your skin to be thick enough to take criticism, but not so hard that you can't feel it. If you go into your first submission too hopeful that they will recognize your genius immmediately, then you will suffer too deeply when they reject you. Expect them not to "get it" on the first try. And expect also that you may not yet know enough to make your results interesting to your future peers. Let them tell you why they don't want to publish your work in its current form. Then try again.
And again, and again. The exchange of words between you and your field's journals is one of the ongoing conversations you should be having while you learn your craft. Once you get used to it, it can be a very enjoyable, very constructive experience to hear what your editors and reviewers think. When you meet them at conferences you will usually find that they were much more sympathetic to your work than you thought when you read their "rejection". They really did mean that you should continue to think of their journal as an outlet for your work.