Displaying recent posts from another site on your own site is easy. If the other site uses Feedburner, you can simply paste this code in any widget area using a text widget.
Using Feedburner Buzz Boost
Grab your own code from Feedburner.
Simply change the conditional tag, hook and Feedburner url.
And don’t forget you can use the default RSS widget by adding the feed address to the widget.
The other site doesn’t need to be using Feedburner as all WordPress sites offer a default feed address like http://yourdomain.com/feed.