IMPORTANT EDIT

This has unknowingly came to my attention as it slipped my mind, PHP 5.4 have already reach EOL and the last security support was stopped on the 14th of September 2015.

According to official documentation, PHP 5.5 will finally reach its EOL on the 10 of July 2016 (Active support has already been stopped but this version will still get security updates until its final EOl date of 10 of July 2016).

So to come back to the original question, you should be running on minimum at least PHP 5.5 now, but be sure to get ready to switch to PHP 5.6 within the next 8 months as from date of this answer

ORIGINAL ANSWER

Wordpress are still stuck on the dinosaur PHP versions, so any PHP version newer or equal to 5.3 should do.

It is however very very important to note that all PHP versions prior to version 5.4 have been EOL'ed, the last version being 5.3 a year ago. In short, this means than any PHP version older than 5.4 are no longer supported or updated, which will cause huge security issues if you are still using it.

So, for safety, the bare minimum you should be running safely is PHP 5.4.x, where x should be the latest security release.

In short, to be rather safe than sorry, just like Wordpress, it is always always the best to have the latest available stable release installed.