Koi need room (large, deep ponds) and filtration systems, and can grow quite large in the right conditions.  They can make a mess by knocking over plant pots, and sometimes eating the plants.  Alternatives for those with smaller ponds include Sarasa Comets, Shubunkins, and common goldfish.  

These are just a few of the options you have under the Fancy Goldfish category:

Visit the Bristol Aquarists Society page for information on these pretties, and many more.