Rather than edit the layout xml files and risk problems during an upgrade, it’s best to use local.xml in your design package default directory. The first use of this file is to prevent blocks from appearing. Simply add the following code with the relevant block listed.

<?xml version="1.0" ?>
 <layout>
  <default>
   <remove name="left.permanent.callout" /> <!--the dog-->
   <remove name="right.permanent.callout" /> <!--back to school-->
   <remove name="catalog.compare.sidebar" /> <!--product compare-->
   <remove name="paypal.partner.right.logo" /> <!--paypal logo-->
   <remove name="cart_sidebar" /> <!--cart sidebar-->
   <remove name="left.reports.product.viewed" /> <!--recently viewed prod-->
   <remove name="right.reports.product.viewed" /> <!--recently viewed prod-->
   <remove name="right.reports.product.compared" /> <!--recently compared prod-->
  </default>
 </layout>

You can find the names of the blocks by viewing the appropriate xml file. To find the xml file, turn on the developer hints and look at the directory listed after the template directory. This is the xml file. Locate this in your base package and note the names of the blocks you want to prevent from appearing.

Here’s an example from classyllama.com:

<?xml version="1.0"?>
<layout version="0.1.0">

<default>

	<reference name="head">
		<!-- Magento looks in /skin/frontend/<INTERFACE>/<THEME>/js/buyprinting.js for this file -->
		<action method="addItem"><type>skin_js</type><name>js/buyprinting.js</name></action>

		<!-- This removes the item that was set in the page.xml file -->
		<action method="removeItem"><type>skin_js</type><name>js/iehover-fix.js</name></action>

		<!-- Magento looks in /js/prototype/element.storage.js for this file -->
		<action method="addJs"><name>prototype/element.storage.js</name></action>

		<action method="addCss">
<stylesheet>css/buyprinting.css</stylesheet></action>
	</reference>

	<reference name="header">
		<!-- This adds a CMS block that can be called from the template file
		associated with the header block. -->
		<block type="cms/block" name="cms_quick_help">
			<action method="setBlockId"><block_id>quick_help</block_id></action>
		</block>

		<!-- The remove tag removes the blocks with the specified name from the layout -->
		<remove name="top.menu"/>
		<remove name="store_language"/>
		<remove name="breadcrumbs"/>
	</reference>

	<reference name="top.nav">
		<remove name="catalog.topnav"/>
	</reference>

	<reference name="left">
		<remove name="left.newsletter"/>
		<remove name="left.permanent.callout"/>
		<remove name="catalogsearch.leftnav"/>

		<!-- When you use the remove tag, it removes any blocks with the specified name from
			the entire layout, regardless of the context. So, if I remove right.newsletter in
			the <default> context and that name is used in say the <catalog_product_view> context,
			then both blocks will be removed.  Because remove operates on the global context,
			you can only remove an element once.  Since <remove name="right.newsletter" /> is
			being called in catalogsearch.xml, we have to unset it, or else we'll get an error.

			The line below only unsets the block from the parent's context, not the global
			layout context -->
		<action method="unsetChild"><name>right.newsletter</name></action>
	</reference>

	<reference name="right">
		<!-- Some blocks have to be removed using remove, others via unsetChild.
			I've not spent the time digging into the code to figure out why -->
		<remove name="right.permanent.callout"/>
		<remove name="catalog.compare.sidebar"/>
		<remove name="left.reports.product.viewed"/>
		<action method="unsetChild"><name>sale.reorder.sidebar</name></action>
		<action method="unsetChild"><name>wishlist_sidebar</name></action>
		<action method="unsetChild"><name>right.reports.product.viewed</name></action>
		<remove name="cart_sidebar"/>
	</reference>

</default>

<!-- CATALOG PAGES -->
	<catalog_product_view><!-- 2columns-right -->
		<reference name="root">
			<action method="setTemplate"><template>page/2columns-left.phtml</template></action>
		</reference>
		<reference name="content">
			<reference name="product.info">
				<block type="cms/block" name="cms_product_info_tabs">
					<action method="setBlockId"><block_id>product_info_tabs</block_id></action>
				</block>
				<block type="catalog/product_view" name="product.clone_prices" as="prices" template="catalog/product/view/price_clone.phtml"/>
				<action method="unsetChild"><name>tierprices</name></action>
				<action method="unsetChild"><name>addto</name></action>
				<remove name="addto"/>
				<reference name="product.info.options.wrapper.bottom">
					<action method="unsetChild"><name>product.tierprices</name></action>
				</reference>
			</reference>
		</reference>
	</catalog_product_view>

</layout>