I have made edge grain and end grain boards using lumber from 12/4 thick down to under 3/4.
Thinner stock stock just means more glue ups and more chances for mis-alignment that will have to be flattened out once the glue sets up.
I am assuming you have decided to go with a face or edge grain cutting board. If so I would use 8/4 wood. I don't think laminating two slabs of 4/4 would look right (just opinion). If going with end grain then the thickness of the stock shouldn't matter much, you will just have more and smaller sections or blocks to glue up. You could make it as thick as you want. 8/4 would always be easier I think whatever way you go (like Mark said)