I think Rick Blute (+ collaborators) has done some things with this. It is not clear whether you want a self-duality or a *-autonomous category. If you stick to finite dimensional Hilbert spaces, the situation seems simple. If V and W are inner product spaces, then for f, g: V --> W, let f.g = \sum f(v_i).g(v_i) the sum taken over an orthonormal basis. I believe this is invariant to an orthonormal base change and it is obviously positive definite. For infinite dimensional spaces, you would have to stick to f for which \sum f(v_i)^2 < oo. But this isn't a category. It is closed under composition (I think) but certainly lacks identities. This gives rise to something called a nuclear category. The category has all maps and there is sub-non-category of nuclear maps. This all goes back (needless to say) to Grothendieck. If by *-category you just mean self dual, well then Hilbert spaces certainly are that. Self dual categories are a dime a dozen. Just take C x C^op. The amazing thing is that if C is closed, C x C^op is *-autonomous, (assuming C has binary cartesian products). Michael