We have site pages stored in the document library. Is there a way to hide the breadcrumb which appears in the page (outofbox) site->document library->page name?
You can create a CSS file that sets the
display:none rule for the breadcrumb itself. The specific selectors you need would depend on your site but you can find those using either the IE Developer toolbar in IE or Firebug in Firefox. It may take some experimentation to find the exact Selector.
Once you create the CSS file, place it in the /Style Library/CompanyName/CSS/ folder in the site collection. From there, go to the root of the site collection, select Site-Settings-Look and Feel - Master Page. At the bottom of that page is an 'Alternate CSS URL' and you can enter the path to your new CSS file there. Be sure to click on the "Reset all subsites to inherit this alternate CSS URL" checkbox below it so that all subsites pick up the change.
There is a lot more information on this available here.
There is no oob way. If you would use page layouts (requires publishing features) you could do it easily in your page layout. For site pages the only common thing is the master page. Within the master page you can modify it, so that you delete the breadcrumb from the content place holder. However, then it would no longer be visible on any site/page within that site collection.