Anything he wants. (Sounds like a punch line, doesn't it?)
Well, no, really, he wears something that matches the wedding’s level of formality. All guests do. For every level of formality, that's a black suit.
However, because he is such a high-profile guest -- and because he and the FOB will be in a lot of photos with the groom later, they are often asked to rent the same formal wear that the guys in the wedding party get. Sometimes that request is actually seen as a mark of respect and inclusion.
My husband put our dads in the same cutaways, but assigned them black cummerbunds and ties so they’d look a bit different from the groomsmen (red) and from him (white).
What are your dads wearing?