I spotted this thread in the WordPress.com support forum today:
The Links section was removed from the core WordPress.org software, which means that it will probably be removed from WordPress.com soon.
In preparation for that, new blogs no longer display the Links section.
Instead of using Links and a Links Widget, I recommend creating a Custom Menu and a Custom Menu Widget.
See this for more info and a video tutorial: http://en.support.wordpress.com/menus/