UPDATE: Oculus have released their final recommended hardware. Which as I forecast is almost identical to below.

Last week Palmer Luckey indirectly stated the recommended PC hardware specification for the Oculus Rift CV1.
Palmer was initially responding to rumors of a May 2015 release of CV1 which he denied. The rumors stemmed from an interview with Max Planck, the Technical Director of Oculus' new Story Studio. Max mentioned during the interview that "May is getting close" as well as other apparent inaccuracies.

Although we don't get the actual date. I'll take the hardware they're running their public demos and internal prototypes thank you very much. Palmer states they run their demos on Falcon Northwest Tiki machines. For those not familiar with PC builders, Falcon are considered a high end custom PC builder. 
The Falcon Northwest Tiki they use is apparently around $2,000 and includes a NVIDIA GeForce GTX 980. In fact the Tiki only takes one graphics card so SLI is not even possible. Heading over to their configuration page I configured a Tiki as close as I could to $2,000 with a GTX 980 included. Essentially it is the base model Tiki with a Core i5 4950 3.3 GHz, 8GB of 1866MHz memory, GTX 980 4GB and 256GB SSD costing a total of $2,284. The specification is as follows:

• Power Supply
  SilverStone® 450 Watt SFX
• Motherboard
  Asus® Z97I Plus
• Processor
  Intel® Core™ i5 4590 3.3GHz
• Processor Overclock
  No Processor Overclock
• Processor Cooler
  Asetek® Liquid Cooling - Tiki
• Memory
  1866MHz 2x4GB (8GB)
• Video Card
  NVIDIA® GeForce® GTX 980 4GB
• Sound Card
  On-Board Audio
• Networking
  On-Board Ethernet
• Operating System Drive
  Micron® M600 SSD 256GB
• Optical Drive
  Slot-Load DVD Writer
• 64-Bit Operating System
  Microsoft® Windows 8.1

Of course you can build or purchase a machine with a similar specification for less than $2,000. Falcon are the Mercedes/Jaguar[Insert your favorite brand] of the PC industry.
For example. Something like the following would be a good starting point:

Recommended Hardware Build For CV1
Part	Component	Price
Case	Corsair Vengeance C70	$110
PSU	SeaSonic G-750 SSR-750RM 750W	$114
Mobo	GIGABYTE GA-G1.Sniper Z97	$174
CPU	Intel Core i5-4950 3.3GHz	$199
Cooler	Cooler Master Hyper 212 Evo	$35
GPU	EVGA GeForce GTX 980 4GB 256-Bit GDDR5	$549
RAM	2x 4GB G.Skill Ripjaws F3-12800CL9D-8GBXL	$62
Optical Drive	Samsung SH-224DB/BEBE DVD Burner	$20
SSD	Crucial MX100 240GB	$104
HDD	Seagate Barracuda 1TB ST1000DM003	$52

This comes to a total of just $1419. Far less money but less sexy too. However the money saved will likely buy you a CV1

Since the Crescent Bay Prototype is expected to be pretty close to the final version (With polish and perhaps motion tracking). It is very safe to say one high end graphics card and a decent PC is going to be enough for a good VR experience.

Palmer Luckey on Reddit:

"There is a lot of incorrect information in this article - Max is a new hire, and he was definitely off on many things. While he is a technical director at Story Studio, he is not directly involved with Rift, nor is he an expert on many of the associated technologies like tracking or low-persistence. I can't clarify with concrete info on a lot of these yet, but suffice to say that May is no special month for the Rift, nor do we have price locked down for CV1.

As a more concrete example, we run everything (including internal prototypes) off a regular Falcon Northwest Tiki with a regular GTX 980, which is our preferred rig for shows as well. They cost ~$2,000, not $10,000, and are one of the smallest gaming PCs you can buy.

Same goes for wires and tracking technology - we are always researching new things internally, but we are a long ways away from wireless video transmission and alternative tracking technologies getting good enough from VR. I doubt anyone wants CV1 held up for tech that may never come!"

You can head on over to Reddit to read the comments. Many of which are amusing. Much of them related to how unlikely it is that Max will be promoted anytime soon!
Moral of the story? Make sure you know your product inside and out. Especially if you're going to be interviewed.

UPDATE: Oculus have released their final recommended hardware. Which as I forecast is almost identical to the above.