This question makes me suspicious... Is this something that didn't happen with your previous monitor? When you say it goes off the screen to the right and bottom, do you mean it is completely obscured and you can't see a single pixel?
Realize that your mouse cursor is just the pixel in the upper-left corner of the arrow. If the cursor stopped before the bottom right of the arrow went off the screen, you would be unable to click on any of the pixels in a 10-15 pixel stripe at the bottom and right of your monitor.
I pose these questions because you mention only having this problem at the bottom right edges and not the top left. However, if the cursor is indeed becoming completely obscured by the edge of the display such that you can't see a single fleck of cursor pixel, I would recommend making sure your computer is configured for just the one monitor, that it's set to the proper resolution, and that it has any necessary drivers. If you take a screenshot is there content off the edges that you can't see on your monitor?
One other option that might be more of what you're looking for is to customize the look of the cursor so that it rotates to stay inside the screen when moving towards the edges. I'm not familiar enough with Windows to suggest anything, but maybe someone else can help, or Google "windows cursors" or something.
DO you mean, off the right edge of the screen? Really far as if you had another monitor next to the current one? if its a little you might want to try this:
http://www.softpedia.com/get/PORTABLE-SOFTWARE/System/System-Enhancements/Windows-Portable-Applications-Portable-CursorUS.shtml
As far as I know every PC I've used in history has done that. I just got in the habit of moving my mouse in the upper-left direction if I lose it. – vcsjones – 2010-12-26T01:30:12.097