Will a standard home automatic circuit breaker, designed and sold as to work on 230V AC (alternating current), and for example 16A, or 25A etc, will it work (break the circuit if it exceeds the rated amperage) on 12V direct current (DC)?
If not, are there any automatic circuit breakers for over-current protection, which work on DC? I mean besides fuses which blow, I want the thing to be reusable with a click, not one-time-use.
Use one designed for low voltage DC such as Eaton KD1 or this automotive type. A better option is also a Raychem Polyswitch which self resets when the current is removed. The problem with the 230V ones is the high trip current, have you really got more than 16 or 25 amps available from your 12V supply?
Edit: I didn't realise this related to an earlier question where you are talking about an automotive battery. In that case, yes, many amps are available (as opposed to a wall wart), and Andrew's comment applies - a breaker designed for AC should not be used on DC because it is a harder job to seperate the contacts on a DC current than on AC where the magnetic field falls to zero repeatedly due to the waveform.
MCBs (and fuses) have a characteristic curve showing time to trip against overcurrent. At the rated current, they should last indefinately, but as that is exceeded they trip faster. For a fast trip, you need the source to be capable of many times the rated trip current.