In Normal view, click on the break to select it, then press delete. Gone.
If it is just a page break, you'll probably close up the space you mentioned,and that will be that. However, if it was a section break, as used between portrait and landscape pages or to restart page numbering or change header/footer information, you may need to keep it.

You can also see which kind it is in Page Layout view by going to Tools/Options and checking the Hidden Text box on the View tab. The keyboard shortcut for toggling this on and off is Ctrl+Shift+8.