If you login to your WordPress website you will see a notice about the new WordPress 3.4 release. If you want to start a new WordPress website, this release is the new stable version.
There are several great improvements in this release, like the theme preview function.
With this option, you can check how your website would look with a new theme, and you can change configuration options without activating the theme!
Besides this theme preview you also get better performance and better image handling with captions. You can now place HTML code like a link into the caption field.
Do I Need to Upgrade?
It is always a good idea to keep up-to-date with a new release, but make sure you first make a good back-up. You can then always revert back if you run into trouble with a theme or a plugin that is not compatible.
I will update some minor WordPress website first and take it from there.
Be Carefull, if you changed the standard Twenty Eleven theme, make sure you back it up. This new version will overwrite your changes!
If you want to read more on the new features, like the embedded tweet function, go to http://wordpress.org/news/2012/06/green/
Together with some good performance updates definitely a fine update, so go ahead and try the new WordPress 3.4 Green Release on your blog / website.