See the wiki which says the minimum level is 5.4+
But see this linked page from the wiki which recommends 5.6 with a bare minimum of 5.3.10.
See also the system status for release 4.7 which says the minimum recommendation is 5.5
Which is it?
CiviCRM PHP requirements recommends PHP5.5 or greater, and notes PHP5.3.10 is the bare minimum required. As well as this, you want to be sure your PHP version is actively getting security updates, and also consider what PHP versions CiviCRM is tested with.
As of Feb 2016, I recommend PHP5.6 -
NB: Distributions may backport security fixes for older versions after those dates; please do your own diligence on whether your PHP version is secure :)
Chris' answer is correct. However, a coworker reported at least one instance of an extension that did not run correctly on PHP 5.3 (I'm afraid I don't know which), so this answer applies to core CiviCRM only.