Since you have a relatively static header and footer, those would be easiest. Just take all the header code (all the way up to <html> if you want) and put it into a separate "header.php" file, the same for footer, put it all into a separate "footer.php" file. Then on all of your pages, replace your header and footer code with <?php include('path/to/header.php'); ?> at the top, and <?php include('path/to/footer.php'); ?> at the bottom, and it will include the content of those files in your document, as if the code was there in the first place. That way you only have to edit one file when changing the header/footer. Don't forget to rename all your pages to .php so the tags work!
I noticed you split up sections into their own subdirectories, like /games, /apps, etc. So you'd need to use include('../header.php'); if you store the header file in the root directory, as '../' will move up to the parent directory.
And last but not least I see you use class="current" to denote which topic is selected. With the header code repeated on each page you can easily modify it to do that, but with it in one location as an include, it's a bit more tricky since the code will have to be the same on each page it's included on. If you don't want to muck up your pages too much, one simple solution would be this:
At the top of every page, you'd have two lines.
Code:
<?php $page = 'Home';
include('header.php'); ?>
In the first line, just replace 'Home' with whatever page you want to be underlined in the navbar. Then, in the header file, use this code for the menu:
Code:
<ul id="menu">
<li<?php if($page == 'Home'){echo ' class="current"';}><a href="index.html">Home</a></li>
<li<?php if($page == 'About'){echo ' class="current"';}><a href="about/index.html">About</a></li>
<li<?php if($page == 'Games'){echo ' class="current"';}><a href="games/index.html">Games</a></li>
<li<?php if($page == 'Apps'){echo ' class="current"';}><a href="apps/index.html">Apps</a></li>
<li<?php if($page == 'Projects'){echo ' class="current"';}><a href="projects/index.html">Projects</a></li>
<li<?php if($page == 'Other'){echo ' class="current"';}><a href="other/index.html">Other</a></li>
<li<?php if($page == 'Links'){echo ' class="current"';}><a href="links/index.html">Links</a></li>
<li<?php if($page == 'Contact'){echo ' class="current"';}><a href="contact/index.html">Contact</a></li>
</ul>
That way, whatever page you set before including the header will be the one underlined. It's a little dirty, but would be easiest to implement with the current pages you have set up.