Crack "thickness" is an imprecise term. Cracks are usually characterized by width and depth. There are no hard and fast rules for what is an acceptable crack width or depth. All reinforced concrete structures contain cracks. Cracks should be distributed, rather than concentrated. Acceptable crack widths and depths should limit the effects of corrosion, which in turn depend, inter alia, on the exposure conditions, concrete cover, rebar coating (used in North America for bridges where salts are applied for de-icing).
Standards such as ACI (American Concrete Institute, Eurocodes) provide guidelines for how to protect reinforcement from corrosion.
Be extra careful when designing structures exposed to a warm moist marine environment.
Cracks depends on specific factors such as type and purpose of the structure, location of the crack and the environment in which the structure is situated. Perhaps hairline cracks which is less than 0.3mm wide are very thin and barely noticed are considered to be acceptable in most cases.
Larger cracks may be acceptable or not depending on circumstances. Cracks up to 3mm in width are acceptable for residential buildings while 1.5mm or less may be acceptable for commercial and other types of buildings.
As per IS Code following is recommended:" The surface width of the cracks should not, in general, exceed 0.3 mm in members where cracking is not harmful and does not have any serious adverse effects upon the preservation of reinforcing steel nor upon the durability of the structures. In members where cracking in the tensile zone is harmful either because they are exposed to the effects of the weather or continuously exposed to moisture or in contact soil or ground water, an upper limit of 0.2 mm is suggested for the maximum width of cracks. For particularly aggressive environment, such as the 'severe' category, the assessed surface width of cracks should not in general, exceed 0.1 mm.
However, one must remember that crack width is proportional to average steel strain at the level considered and therefore one may notice that in working stress the permissible values are decreased for bridge design and further reduced for water tanks design.