Amino acids exist as zwitterions when they are at their isoelectric point (also known as the pI value).  This is the pH at which the amino acid has both a negative charge (on the carboxylate side of the molecule) and a positive charge (on the amino side of the molecule).  Overall, it is a a neutral molecule, but it has both charges present within the structure.  The charges are always +1 and -1.

This is only true for amino acids at that particular pH.  When the pH changes, one of the ions goes away.  At low pH values, there is an excess of H+ ions present resulting in the protonation of the negative ion so the amino acid has a positive charges.  At high pH values, there is an excess of OH- ions present resulting in removal of the proton from the carboxylic acid side and as a result, we end up with a negative ion.