It is true for arbitrary products of model categories (or just cofibration categories) as proven in Theorem 7.1.1 of http://arxiv.org/abs/math/0610009v4.

It is also true for finite products of arbitrary relative categories as discussed in this answser: http://mathoverflow.net/questions/44047/localizing-an-arbitrary-additive-category/44155#44155. (For more details on this and related arguments see http://nforum.mathforge.org/discussion/4769/connected-components-preserve-finite-products/.)