Allowing the user to choose the hashing formula at the registration I was thinking of a potential new way to increase someone's account security.

The idea was allowing the user to choose one of the hash formulas available in the software (example: "MD5", "SHA512" and "Whirlpool"), decreasing the chances of any intruder to find out the hashing system used in case passwords are — for some reason — leaked increasing a potential required time of brute-force or dictionary attacks.

Would that be a good idea?
This doesn't sound like a good idea. As CodeInChaos already pointed out, choose one good password hashing scheme like scrypt or bcrypt and go with that

The reason why what you proposed isn't so great is that you'll give the user the choice between a few good password hashing options and the work of an attacker is at best multiplied by the number of options you proposed. 

By doing that it's also unlikely that a bad password hashing will make its way into the list and the users picking that one will be at the attacker's mercy.
Lastly I don't think it's a good design to leave security relevant choices up to the user. 

How should an average user know better than the designer of the system what's good for him ?