Sony has just started pushing PS4 firmware 6.51 to PS4 consoles worldwide.
PS4 6.51 and hacks

As always with such a minor release, not much is known about the update. It is not clear whether this actually patches an undisclosed exploit, or if it just brings some urgent patch for a specific game. Furthermore, at the time of publishing, Sony haven’t updated their official firmware page and 6.50 is still mentioned as the latest update.

We advise for people who want to hack their console to stay on as own a firmware as they possibly can, until we hear more details from hackers. The highest hackable firmware (publicly) is 5.07. (Check more details on our PS4 Jailbreak page)
PS4 6.50

The previous update, PS4 firmware 6.50, was released 3 weeks ago and added remote play support for iOS as well as the possibility to swap the O/X buttons.
Should I update my PS4 to 6.5x?

Again, for people willing to hack their console should stay on a low firmware if possible. Hackers have hinted at hacks available on firmware 6.xx, and there even was a webkit exploit released for 6.20, but no “full” Jailbreak has been announced for recent firmwares by any credible source.
For people not looking to hack their PS4, it is likely you will have to update to 6.51 in order to retain online service access for your console (PSN, etc…)