What is Viiv? Marketing.
Viiv is Intel's "Home PC" equivalent of Centrino. It is a marketing term made up to describe something that already exists; only in order to use the marketing term, you have to use all Intel equipment. (They also have a business-PC equivalent, "vPro".)
Viiv is simply a label that PC manufacturers can slap on any computer that uses an Intel dual-core processor, Intel main chipset, Intel network chip, and has 'Media PC' capabilities (basically, any PC that uses Microsoft's Windows Media Center Edition OS.) If Intel were to allow Front Row as an acceptable replacement for Media Center, and Apple were to use Intel network chips instead of whomever they use now, the iMac and Mac mini at least would qualify.
Intel just offers some web-based benefits to computers that qualify as 'Viiv' computers. Just like when the Pentium 3 first came out, they offered some web-based stuff to Pentium 3 owners, even though there was no technical reason why the stuff wouldn't work with other computers. (Like Skype's 10-person conferences that were artificially limited to Intel computers.)
Just like Centrino. Centrino just means Intel Pentium-M or Core (x) Solo/Duo processor, Intel chipset, and Intel wireless card. Apple doesn't use Intel wireless cards, so MacBooks and MacBook Pros don't qualify as Centrino. (As an example, I bought an HP laptop that came with a Celeron-M processor, but DID have an Intel wireless card. It was not 'Centrino' qualified. All I did was upgrade the processor to a Pentium-M, and now it passes Intel's Centrino test utility.)
Does this marketing work? Well, the jury is out on Viiv, it doesn't seem to hold the same cache as Cenrino. But, my dad works at a large nationwide company, and is the person who orders all new hardware and software, company-wide. When Centrino first came out, a VP told him he wanted a Centrino laptop because it was good. My dad told him that all their new laptops had Pentium M processors, and had third-party 802.11a/g hardware, when at the time, Centrino was 802.11b-only. So the hardware they were buying was BETTER than Centrino. This VP insisted that Centrino was better, because the ads in his executive magazines said so, so he wanted a Cenrino laptop. Well, the manufacturer that the company had contracts with didn't offer 'real' Centrino laptops yet, so my dad had to go order them from a different manufacturer, making this VP the only one in the company with his model of laptop. Well, a year later, when the laptop broke, he had to wait a couple weeks for a replacement, since they didn't have in-company spares, the way they did with the non-Centrino models.
Epilogue: Will we see 'Viiv' in Apple products? Not a chance. Apple hates using other companies marketing terms, just look at 'Altivec'. Apple invented their own term for Motorola's vector instruction set, rather than use Motorola's name. Apple can get support hardware (network cards) cheaper when they go through third party companies, the way they do now with both wireless and wired network cards, which would make their products not qualify as 'Viiv' or 'Centrino' anyway. Apple already eschewed 'Centrino', which would have brought marketing dollars from Intel; why would they use Viiv? There is no technical anything behind Viiv, just marketing. And Apple prefers to control their own marketing. (Plus, Viiv isn't even publicly known that well. Centrino was already a major 'brand', so if they weren't going to go with a known brand, why would they throw their weight behind an unknown one?)