If you have a requirement to remove breadcrumb from certain pages say the Magento CMS Pages then you can simply follow the 2 steps:

Step 1: Create a “local.xml” file in your custom theme layout folder

Add the following content to the local.xml file

<?xml version="1.0" ?>
<layout version="0.1.0">
<cms_page translate="label">
<reference name="root">
<remove name="breadcrumbs"/>
</reference>
</cms_page>
</layout>

To cut it short you can put the above as

<?xml version="1.0" ?>
<layout version="0.1.0">
<cms_page translate="label">
<remove name="breadcrumbs"/>
</cms_page>
</layout>

Step 2: Flush the Magento Cache

Now refresh you page and enjoy!