The latest requirements for Drupal 8 include a requirement for MySQL/MariaDB/PerconaDB of version 5.5.3 or later - now THAT one may be an issue for a lot of hosting companies. We're going to get that done, but it's a little more unusual than the PHP requirement. At the moment our solution to this is to be using CentOS 7 for all of our database servers (and since CentOS 7 uses MariaDB 5.5, that works fine). We're currently re-thinking what we're actually going to do about this before the Drupal 8 release.
I'm writing a little bit today about some of the concerns that folks are having about Drupal 8, the new hosting requirements it imposes, and particularly the concerns that smaller organizations will not be able to find Drupal 8 compatible hosting plans. There is a lot going on with us and with other hosting companies at the moment to support Drupal 8 and other PHP software that has more modern requirements. We don't think this will be an issue with most reliable hosting companies by the time Drupal 8 ships.
First of all, as they stand, the requirements are really not that onerous. There was an announcement today that the new minimum required PHP version is 5.5.9. This is really not such a bad requirement, though I'll admit that not all hosting companies have PHP 5.5 available. Our newer server builds all include an option for 5.5.21 - and in fact we're planning on shortly making that the DEFAULT PHP version for new hosting plans - people who need a lower PHP version will need to explicitly set it. We are currently supporting 5.5 and 5.4 on all of our servers, and if you require 5.3 we can assign you to one of our legacy servers that still supports that. I am sure that as time goes on, more hosting companies will be supporting newer versions of PHP to support newer CMS systems.
I tihink the primary concern here will be that Drupal 8 so far appears to have a bigger memory foot print than 7, and that may well cause some issues since most lower-cost hosting systems may not allow PHP instances large enough to support Drupal 8 once it has more than a few modules enabled. Though some work is currently going on to lower the memory footprint of Drupal 8, it looks pretty likely to be bigger than 7 (which is not surprising considering how many new goodies it includes).
We have been doing testing of Drupal 8 on our shared server plans, and so far have not had any real issues. It's our intention to have a supported Drupal 8 hosting plan by the time Drupal 8 ships. This plan will have extended memory allowances, will have PHP 5.5.21, as well as the other features we already support such as memcache, opcode caching (well, that's a no-brainer since it's included in PHP 5.5) and on the Drupal 8 plans, access to a MariaDB server with InnoDB as the default database engine, and free Cloudflare support. All of this at an affordable price (though slightly higher than our current shared hosting plans). Help is on the way as we re-structure some of our hosting plans to support some of the newer features that our clients will require.