EpubTest.org is a joint project of the IDPF, the BISG, and the DAISY Consortium, and it was developed to enable readers and developers to collaborate and share information on which Epub 3 features are supported by which popular ebook platform.
It includes a suite of Epub3 ebooks which you can download and use to test your preferred reading app. That test suite has been under development since October 2012, and it's grown to include a collection of 20 Epub3 files, each designed to test a different part of the Epub3 spec. They're available for download for free (no registration required).
In addition to the test suite, the site also has a page full of detailed descriptions listing Epub3 support for iBooks, Kobo, Google, Kindle, and other ebook platforms. According to that page Google Play Books supports just under half of the Epub3 spec. Kobo scored about 60% on their iOS app, but their tablets and ereaders only scored about 45%.
I don't see any test results for iBooks, but there are a number of other major and indie ebook platforms listed. Of the major platforms, the Nook comes in a distinct last place, with the Nook Android app earning a score of only 16%. A number of indie platforms, including Readmill, Helicon books, and Bluefire, scored significantly higher than the Nook Android app. And so did the Kindle app on the Kindle Fire HDX, in fact.
The Epub3 ebook standard was finalized by the IDPF in October 2011, but as you can see from the test results support is still more symbolic than actual.