My stylesheet is running through some XML that contains tags like this:

<title>This is <b>My</b> Title, from <i>The History of Eric</i></title>

What I need to return is this:

<header>
This is My Title, from The History of Eric

(yes, no closing tag for header; it's not real XML that's being output.)

How would I go about stripping out the <b> and <i> tags?

Assuming you are positioned on the node containing title: --

Joe (Microsoft MVP - XML)

Try using <xsl:apply-templates/>, it'll basically output the text.
eg.
<xsl:template match="title"/>
<xsl:apply-templates/>
</xsl:template>

Thanks.