TYPO3 Core

The title says it all:

PHP 5.5 will receive security updates until June 2016: http://php.net/supported-versions.php

TYPO3 6.2 was meant to receive security updates until October 2016:
https://typo3.org/news/article/typo3-cms-agenda-more-long-term-support/
/ http://typo3.org/fileadmin/t3org/documents/TYPO3_Release_Agenda_LTS.pdf

now apparently even until beginning of 2017:
https://forge.typo3.org/projects/typo3cms-v62/wiki/Long_Term_Support

This means that if TYPO3 6.2 will not be modified to get PHP 5.6
support, then users would have to run an outdated, unsecure PHP
version for quite a while if they want to keep running the still supported TYPO3 6.2 LTS instead
of 7 or 8.

One of the things which do not work on PHP 5.6 is unserializing empty objects in the extbase 6.2 persistence layer (http://php.net/manual/de/function.unserialize.php), but http://php.net/manual/de/reflectionclass.newinstancewithoutconstructor.php can be used from PHP 5.4 on.

There might be more issues with running TYPO3 6.2 on PHP 5.6.