It does, and the previous version actually did support Occulus. They released a free plugin for it (the free version of Unity) a few months ago.

So for Oculus, both Unity and UnrealEngine are free to use up to $100k/company/year and $3k/product/quarter respectively. Beyond that $75/mo or $1500 for Unity or 5% for UE4 seems small enough to just use the product that's better for your use case. Right now UE4 works better with Oculus timewarp feature. The same on Unity5 apparently suffers from jitter.

With Unity 4, only the Pro version supported the Oculus Rift plugin, because the Rift SDK relies on render-to-texture support, which was disabled in the free version.

Now the free version of Unity also supports the Rift. That is indeed new.

EDIT: I am totally wrong!

Nope, they specifically released a Rift plugin for the Free version of Unity 4 just a few months ago. http://blogs.unity3d.com/2014/12/23/calling-all-vr-enthusias... With full lens correction that needs render-to-texture. Render-to-texture is still disabled in Unity 4 Free, but it is specifically allowed just for the Oculus plugin.

Oh, I stand corrected! Thanks for clarifying.