Why are salt crystals stable if Na+ and Cl− are electrically neutral?

[neginf]

Is the combination of an positive sodium with a negative chlorine neutral ?
If so, what attracts and holds together other sodiums and chlorines to make a grain of salt ?

 

[Borek]

In the crystal lattice each sodium ion is surrounded by six chloride ions, each chloride ion is surrounded by six sodium ions - and they all attract each other.

http://departments.kings.edu/chemlab/animation/nacl.html

 

[Horseb0x]

This picture should explain it
http://www.chemistry.wustl.edu/~edudev/LabTutorials/Water/PublicWaterSupply/images/nacl.jpg
NaCl doesn't exist as just one Na+ ion bonded to just one Cl- ion. Its millions of Na+ cations and Cl- anions ionically bonded to form a lattice like that.

 

[DrDu]

Even though a hypothetical molecule NaCl is neutral, it has a strong dipole moment and higher multipole moments which lead to a strong attraction of the molecules which can serve as an alternative explanation of how the crystal is formed.