A tongue twisters is a logical (more or less) series of words that test a speaker’s ability to pronounce properly. Ideally, a tongue twister forces the speaker to say one word at a time in order to clearly distinguish it from the following and proceeding similarly-sounding words.
Children (small and big) enjoy testing their mettle with these. The classics that all American children learn are “Peter Piper picked a pick of picked peppers. How many pickled peppers did Peter Piper pick?” and “She sells sea shells by the sea shore.” In my opinion, the most difficult tongue twister in English is “Sixth sheik’s sixth sheep’s sick” which simply cannot be said quickly and coherently. (It is okay to try: I said Big and small children.)
The French have some challenging ones also. Un chasseur sachant chasser sait chasser sans son chien de chasse is a real mouthful, literally. Cinq chiens chassent six chats is not easy while Mon père est maire, mon frère est masseur is just cute, which is also important, since it sounds likes My father is a mother, my brother is my sister but means My father is mayor, my brother is a masseur. (Taken from http://www.uebersetzung.at/twister/#fr)
I am not very impressed with Hebrew tongue twisters. They are cute, but Hebrew is simply too poetic (in sound) to make it difficult to pronounce. The best I have seen is גנן גידל דגן בגן, דגן גדול גדל בגן [Ganan geedel dagan bagan, dagan gadol gadal bagan] meaning A gardener grew a cereal in the garden, a large cereal grew in the garden. If you want to see more, see http://www.alphadictionary.com/fun/tongue-twisters/hebrew_tongue_twisters.html
I will let native Russian speakers tell about their toughest tongue twister. I am also interested in tongue twisters in other languages.