I've been changing the permalink structure for WordPress sites to simply postname, and you can do the same! I'll show you how to generate the redirects you need.
In the past, I've configured WordPress to use the permalink structure Day and Name, which formats the URLs for posts as
/%year%/%monthnum%/%day%/%postname%/. Although I knew that a simple
%postname% would produce shorter, more memorable URLs, I avoided that structure because it had been shown to result in slower performance.
WordPress 3.3 fixed that issue. The 3.3 release notes in the WordPress Codex say, "Use the postname permalink structure without a performance penalty." WPCandy also covered this improvement in the articles Recent commit to 3.3 eliminates performance issues with postname permalink structure and Everything we know about the newly released WordPress 3.3.
So, how do you safely change the permalink structure of an existing site to postname, without breaking all the external links to your posts? You'll probably need to generate redirects to add to your .htaccess file. Renowned WordPress developer Joost de Valk has a generator in his article How to Change WordPress Permalinks. The tool gives you the redirect you need to add to the top of your .htaccess file.