MacBook – The headphone jack on the MacBook Pro just stopped working. How to fix it

It sounds like a hardware problem in the jack. If you can put pressure on the external part of the plug and change it: cause static or breakup it's probably a hardware problem in the jack.

If you had said you only tried one set of headphones then I'd have said it's probably a problem in the headphone plug but if it's multiple phones and speakers then it's probably the jack.

There's a sensor in that jack that monitors if something's in it or not to switch off the internal speakers. The if there's continuous sound, just switching from internal to external the problem may be that sensor. If the sound cuts out from both internal and external once in a while it's probably the jack.

If the MacBook Pro is still under warranty I'd have Apple look at it, they'll swap motherboard to make it right if it's a hardware problem at no cost to you.

(posted as an answer so you can accept it and mark this issue resolved)

Have you checked the Sound pref pane in System Preferences? There's a tab labeled "Output" where (I'd expect, as I don't have a portable in front of me just now) you can switch output between built-in speakers and the headphone jack. If the first toggle doesn't work, toggle it again.