There are generally 5 main ( melanoid ( Melanistic ) , leucistic , wild , the Golden and The Albino )  types of Axolotls, for the colors it is a little difficult to list them all but we can classify them according to these categories:

Leucistic
Golden Albino
Wild Type axolotls
Piebald axolotl - rare color 
Mosaic axolotls -rare morph
Copper axolotl
Lavender or Silver Dalmatian axolotls - rare ones too
Black Melanoid
White Albino
Speckled Leucistic
Rare -Chimera axolotl
Heavily-Marked Melanoid
GFP Axolotls or Green Fluorescent Protein
Firefly axolotls , from Indiana but rare ones too
Enigma Axolotl - very rare axolotls