As per ACI 318-05 the cover is dependent upon the site conditions or the environment for which the concrete is being placed (ie. directly in soil or if you were to backfill later). You would have to look this up because it is completely dependent on these conditions, unlike the BS 8110, as Tariq mentioned above, which only depends on the bar diameter.
To answer your example problem, you cannot go below the minimum cover (for obvious reasons), but I have yet to hear of a maximum you are allowed to exceed the minimum. I would imagine you can't go crazy with extra cover or else you could significantly shift the location of the neutral axis which would change the strength properties of the member. I do not have much experience in the industry as of yet, so there may be a "rule-of-thumb" for this.