Manually Updating Wordpress

Yes.

One caveat: I would NOT overwrite the following items:
.htaccess file (if any)
sitemap.xml
sitemap.xml.gz
robots.txt
/wp-content/

About the wp-content folder: it has inside your themes, plugins and uploads (if any). That's why you should NOT touch it.

Everything else can be deleted and/or overwritten.

WARNING: always make a backup of your database before doing anything!!!
The MySQL database (accessible via cPanel > phpMyadmin) holds all your content: posts, Pages, comments, settings.

HTH

You can also use the automated backup system that WP now offers on the dashboard. Just make a backup first and then let the auto-update do it's thing.

Thanks guys.

I tried to use the auto update a few different times from the dashboard and it never seems to work. That's why I am asking about the manual route.

What do you mean it doesn't work? Exactly what errors are you getting?

First things first - do a full backup of the site in question. Copy all the files and the database before doing the update. Otherwise if the site breaks when you try to update it, you're screwed.

Once backed up, you can do manual updates but they can be a pain. Go to the following page and scroll down to "Manual Update" for the steps on how to do it: Updating WordPress « WordPress Codex

The auto update can be a pain to use depending on the permissions setup on your server. It also over writes the old files.

I just do it manually. I download the new version, look at the changelog, and then just upload the files in the changelog. Takes about two minutes.

Whatever the reason for updating, before getting started it is best to check the current minimum requirements page first to make sure that your web host has the required versions of PHP and MySQL. (If you are not sure, then your hosting provider should be able to tell you.) The next thing to do is to take a backup of your database. All your posts and Pages are held in the database, so you will need to have a copy of it in case, for whatever reason, you change your mind after upgrading and need to go back. If you are not sure how to backup your database, then complete instructions can be found in the WordPress Backups section of the Codex.

The final preparation step is to disable plugins. Now, you don't have to do this, but every now and again a plugin hasn't been updated to work with the latest version of WordPress, and causes a problem after the upgrade. So, it's best to try and avoid that, yes? You can easily disable your plugins by heading to the Manage Plugins page in the Dashboard, changing the "Bulk Actions" pull down menu to "Deactivate" and clicking "Apply".

Now that you've checked that you're ready to update, you've turned off your plugins and you've got your backup, it's time to get started. There are two methods for updating - the easiest is the Automatic Update, which will work for most people. If it doesn't work, or you just prefer to be more hands-on, you can follow the manual update process. For a manual upgrade check out extended upgrade instructions.