OS X supports emoji on 10.7 Lion and above. OS X 10.6 Snow Leopard did not have support for emoji.
*Chrome 41 introduced emoji support, on March 3rd, 2015.
OS X 10.9 Mavericks and above include a handy emoji-picker tool, while OS X 10.8 Mountain Lion and below included an option to add emoji to the Character Palette.
A sample of Emoji characters from OS X 10.9 Mavericks
Images via Emojipedia