Color count, sorted by occurences
Bash + coreutils, 54

7 bytes saved thanks to @manatwork


grep -oE '#\w+'|sort|uniq -c|sort -nr|awk '$0=$2&quot; &quot;$1'

This assumes STDIN input of Imagemagick's .txt format.
Ideone.

If the above input format is too much of a stretch, then we can add Imagemagick conversion from any format:
Bash + coreutils + Imagemagick, 71
convert $1 txt:-|grep -oE '#\w+'|sort|uniq -c|sort -nr|awk '$0=$2&quot; &quot;$1'

Here, the input image filename is passed in as a command-line parameter.