Git GUIs have changed quite a bit since this post. For a more updated list see the Git website.
As Git becomes more popular and widely used a GUI becomes even more important. This was especially important when Drupal recently looked at what version control system it was going to switch to. (If you're interested in the Drupal (unofficial) decision checkout Angie Byrons post on groups.drupal.org)
When I surveyed the Git GUI landscape SmartGit stood above the rest for your standard user.
For Your Average User
Git is an extremely powerful program. Powerful enough that there is a manual called Git for Computer Scientists which dives in really deep. There are advanced features within Git that I can't imagine how to build a GUI for.
That being said, the common features that most of us use can be easily encapsulated in a GUI and SmartGit does just that. For a typical user, including front end developers, weekend warriors, and anyone who just doesn't need the advanced abilities, you have access to it with SmartGit.
And, since it was written in Java it runs on Macs, Windows, and Linux.
The most popular site for public Git repos is Github. The interface is slick, the documentation is easy to understand, and it just works. This is where projects like jQuery and TinyMCE are hosted.
SmartGit provides integration with Github.
If you've provided your Github login information into SmartGit clicking on "Select from Github..." will bring up the list of projects you have on Github and let you clone them to your local system to work on them.
Paying For Commercial Use
SmartGit is not an open source project and it is not free for anyone to use. It's free for non-commercial use but, for commercial use you need to pay for a license.
If you want a GUI for commercial use but are looking to only use Open Source or free software there are alternatives. For your average user none of them is as nice.
I've had the chance to use several Git GUIs. Many of them are great at what they do but are not right for your typical user. SmartGit hits that sweet spot.