with horizontal symmetry?
with vertical symmetry?
with 180 degrees rotation symmetry?

What are the LONGEST words in each category? (Common words are preferred.)

If people are interested in symmetrical words, and ambigrams in general I'd reccomend:
http://www.johnlangdon.net/website/New_Pages/Ambigrams.htm
and the book that John Langdon was commissioned to illustrate with ambigrams, "Angels and Demons" by Dan Brown. 
There are some amazing examples of words with rotational symetry there, including the phrase "Angels and Demons" written with the property of rotational symmetry.
Check it out.