There is no standard, really, but there is popular. For example, 16 mils is popular and presents no challenges to the fabricator. You also need to be sure to provide a large enough annular ring around that hole for the fabricator to avoid problems. I think that an 8 mil annular ring would be ok, so the total diameter of the via pad would be 16 + 8 +8 =32 mils. When you do a plated through hole, you should be specific about what your diameter means. You could specify that the diameter is measured after plating, which means that the fabricator would probably choose an 18 mil drill bit, drill the hole and then plate another 1 mil of copper on the wall of the hole for a net diameter of 16 mils. Or you could specify that the fabricator actually drill with a 16 mil bit and allow them to plate the hole down to around 14 mils or so. If you don't give them any details about what your diameter means, they usually assume you want this diameter after plating.
Blind vias are a bit more complex and you should always consult with your fabricator on appropriate sizes.