Atoms have equal numbers of protons and electrons.  
They are electrically neutral.
 So what holds atoms together to make molecules?
There is a RESIDUAL effect of the electromagnetic interaction due to their
charged constituents,
which causes the atoms to bind together to form molecules,
such as this piece of DNA.
Amazing isn't it - all the wonderful structures of the 
world around you exist because protons
 and electrons have opposite charges.