With the feature freeze for PHP 5.5 long past, I figured it was time I post an update to the popular PHP 5.4 and Drupal 7 question.
So, can Drupal run on PHP 5.5?
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In short, if your site runs on PHP 5.3, it will run on 5.5 as well, go upgrade! (Your dev environment, until a real release is out)
With the short answer out of the way, here are some more details.
With regard to "Does Drupal work on it", very little changed from PHP 5.3, to 5.4 to 5.5. The one issue that showed up under PHP 5.4 was really just PHP being better at telling developers when they were doing something wrong, rather than an incompatibility introduced by PHP. The details of that are well covered in PHP 5.4 and Drupal 7.
No similar new warnings show up with PHP 5.5 though, and while some things have changed, they are highly unlikely to have negative impact on your Drupal site.
One performance concern that was raised with running 5.4 was that APC was lagging behind in support. This will not be an issue this time, as 5.5 now includes a replacement for APC Optimizer+
Drupal 6: By now, most things work well with PHP 5.3, meaning it should work well on 5.5 as well. I have yet to test this myself.
Drupal 7: Runs smoothly, I've encountered no problems what so ever, largely because Drupal 7 was developed more with PHP 5.3 in mind, and any problems discovered on 5.4 have long since been fixed.
Drupal 8: Requires 5.3 from the start, so will work well. I will update the answer when I've tested it myself.
Updates to letharion's answer:
Whilst installing a fresh version of Drupal 7.26 in a PHP 5.5 environment, I was getting the "Set-up database" screen load twice. On the 2nd submission of the form, I would then get a WSOD. Loading the site from the root path gave a 404.
I tracked down this patch (comment #45) which solved the problem for me. As you'll read there, it was due to the way the new PHP caching system works and the caching of the settings.php which stores the database credentials.
I have hit a snag trying to install Drupal 7.26 on Ubuntu 13.10 (php 5.5).
Fatal error: Call to undefined function field_attach_load() in /var/www/d7/includes/entity.inc on line 316
I had to apply this patch - https://drupal.org/comment/7721819#comment-7721819.
Deleted existing database for this install.
Re-created the database and then ran
The problem for me was fixed with that patch.
Fresh install of drupal-7.26
Ran PHP 5.5.9 -got error: "...entity.inc on line 316"
In server-control-panel I changed my Drupal folder to use "PHP 5.4.25". Then hit back in browser, re-entered the install-data, and voila -> up and running...
Installed themes, some modules, created pages; changed back to PHP 5.5.9 -> still working...
Drupal 7: Check all issues with tag php 5.4 or php 5.5 to be sure you are not using any of the modules that still have issues with those versions: https://drupal.org/project/issues/search?text=&projects=&assigned=&submitted=&project_issue_followers=&&&&issue_tags_op=%3D&issue_tags=PHP%205.4%2C%20PHP%205.5.
If your site has any of those modules installed I think it is better to stick to php 5.3 for Drupal 7.
Drupal 6 Add the php 5.3 tag too as some less used or maintained modules still have issues with php 5.3.