What's the difference between Google Chrome and/or Chromium? What are the advantages/disadvantages to each?
There are some key differences between Google Chrome and Chromium. First off, Google Chrome is a commercial closed source product made by Google which is based on the open source Chromium project.
Chrome is not available in the default Ubuntu repositories as it's not open source, however Google makes Chrome available through their own 3rd party repository. Chrome is updated by Google directly, as they run the entire repository and update Chrome on their schedule. Since it doesn't need to be redistributable and open source, Chrome includes things that we can't ship in Ubuntu out of the box, like Flash and H264 support (See the Ubuntu promise). However you can install this support with a few packages (see below).
Chromium, being open source, is available in the Ubuntu repositories. This is maintained by Ubuntu developers and goes through our Stable Release Update process. Chromium has a release process exception, which allows the team to upload a Chromium build as soon as a new upstream release is made.
There really aren't any proper "releases" made of Chromium, so Ubuntu developers base their build on what stable version of Chromium the stable Chrome build is based off of. Fabien Tassin has a blog post about this process that goes into much more detail.
The following packages in Ubuntu install the codecs and features in Chromium that you can find in Chrome:
chromium-codecs-ffmpeg
chromium-codecs-ffmpeg-extra
flashplugin-installer
Really it depends on what you want. If you trust Google to not break your computer and like the convenience of Chrome then you can use that; if you want an open source browser that is the basis of Chrome that is peer reviewed by Ubuntu developers and doesn't require 3rd party sources then you want Chromium.
This Wikipedia page outlines some of the security/usage tracking differences between the two browsers.
The official Chromium Wiki provides a detailed list about the differences between Google Chrome and Chromium. It does not reflect differences of vanilla source versus those that are specific to Chromium packages provided by Ubuntu.
Google Chrome is based on Chromium, the Open Source Web Browser. I've been using both of them and they are 99.99% similar. I finally choose to use Chromium because it's open source. You can still use all the extensions for Chrome, and also sync your bookmarks (and other stuff) with a Gmail account.
If you look at Wikipedia it says that the differences are that Chrome has Adobe Flash Player pre-installed (not open source software) and Chromium not. But you can still install it later very easily. That Chrome has auto-update mechanism, but using Ubuntu you have auto-update (and you can also add the Chromium repository). Also that Chrome has Google's brand and Chromium not (I don't care) and they say something about the colors of the logo (not very intelligent comments). Finally they say that Chrome has click-through licensing terms and usage-tracking. This last thing I'm almost sure is optional.
Use Chromium!