If you find yourself repeatedly receiving messages like:
ERROR: Unable to unpack /public_html/downloader/pearlib/download/some_awesome_module.tgz
After checking permissions (which should be right to have gotten this far) you could try the fix below.
Tar <- download this tar.php file (it’s zipped for your convenience).
Browse to downloader/pearlib/php/Archive and rename Tar.php to Tar.old
Upload the extracted Tar.php from the download above
Now Magento Connect downloads should work fine