If you actually listen to his music, read the lyrics (for the songs that have lyrics), look at the symbolism and iconography he utilizes (and has pretty much always utilized, even as far back as his Zappa days), Vai seems to subscribe to a combination of Judeo-Christian ethics melded with Transcendentalism (of one variety or another), and with a little bit of "Eastern" philosophy tossed into the mix. Oh, and he believes in UFO's...that much is for sure.
I've always found that his spiritualism is a particularly interesting aspect of his personality. It definitely influences (or even defines) his music to one degree or another. He's pretty much the definition of a Zen Guitarist.
EDIT: Oh, and the piles of cash and free guitars from Ibanez don't hurt, either. I would personally find it very easy to reach a different spiritual plane if Ibanez was throwing free axes at me every other week.