I have seen かたつむり and でんでんむし and ででむし listed as "snail." What are the differences between these words?
They are dialectal forms, but it could be said that three synonymous forms かたつむり, でんでんむし, and まいまい have gained more or less nation-wide recognition today. The situation is somehow similar to that "soda/pop/coke" tripartition in USA.
The name of snail has been a signature of Japanese dialectology since the pioneering work 『蝸牛考』 written in 1930 by Kunio Yanagida. The summary of this book is that dialectal forms distribute in concentric circles from Kyoto, so that the remotest place maintains the oldest form.
(newer/nearer to Kyoto → older/farther)
デデムシ > マイマイ > カタツムリ > ツブリ > ナメクジ (source)
I (and most people living in Tokyo) would use かたつむり most often.