Trying to embed a video in a Views Header
The 'Full HTML' format in Drupal 7 by default still strips out some of your tags, check your format settings under Administer » Configuration » Content authoring » Text format, or /admin/config/content/formats/ and you'll see that for the Full HTML format, you're limited to the following tags:

&lt;a&gt; &lt;em&gt; &lt;strong&gt; &lt;cite&gt; &lt;blockquote&gt; &lt;code&gt; &lt;ul&gt; &lt;ol&gt; &lt;li&gt; &lt;dl&gt; &lt;dt&gt; &lt;dd&gt;


You can either add an object, embed tag here to make these work for this input format or you can add a separate input format that has no restrictions. The choice will really depend on what kind of site you are running and who else might have access to this format. If I were letting users use the 'Full HTML' format for adding comments, content, I would definitely want to restrict the tags they use and allow only admins access to an unfiltered format.