for any of Vai's signature Ibanez guitars. I'll throw in some of Dave Meniketti's because they are awesome.
Not a "signature" model, but Dave's '68 Les Paul gold top is absolutely iconic in the way EVH's Frankenstrat is to Eddie. As you can see from the pics, this guitar has seen some
serious playing.
Dave's signature LP-style Biceglia:
I remember when the prototype was being built:
And, finally, not
Dave's personal signature model, but he loves this gorgeous Bonnie Raitt signature strat. I'm not a stratocaster fan, but it is a very nice (and nice sounding) guitar: