This is the fastest way to remove the news from the wordpress admin dashboard.
Open up your favorite ftp program and connect to your blog.
In the wp-admin folder find the file index.php, make a backup of this file just in case u mess it up and you have to restore it later.
Now open up index.php and around line 15 you should find the following:
add_action( 'admin_head', 'index_js' );
Just comment out that line with double slashes like this:
//add_action( 'admin_head', 'index_js' );
Save the file and you`re done!
I only did this to my blog because I wanted to clean it up a bit.
Keep in mind that if you disable the news you will not see the latest updates from “WordPress Development Blog”. This can be a bad thing.
However, if you want to keep the “WordPress Development Blog” news and only disable the “Other WordPress News” do the following:
In stead of commenting out the line like told above, look for this:
It should be around line 10. Just remove it, save the file and you`re done.
I only did this on Version 2.3 so if your version is prior to this it might not work exactly like this but you got the idea. It might not be the best way to do it but it`s the simplest and fastest for me.