I've been using http://wordpress.org/plugins/wp-clone-by-wp-academy/. It works nicely for smaller websites!
Just 3 steps:
- Install the plugin on both sites.
- Use the plugin to generate a backup on the old site.
- Take the backup URL it gives you and plug it into the plugin page on the new site, hit go, and your migration is complete in just a few seconds!
It adjusts all the URLs automatically - including serialized string replacements - so no risk of losing widget configurations, etc.
The only issues I've had are with some websites with larger databases (~300MB), which caused PHP script execution timeouts during import of the site backup.