* "She sells seashells by the seashore." This one isn't quite as old as it sounds, but it's based on a 19th-century English children's rhyme and a much older Greek tongue twister, "The she-goat who bore a she-goat ate ivy."
* "Peter Piper picked a peck of pickled peppers." This one is also based on a much older tongue twister, "The tongue twister that twisters tongues."
These examples show that the concept of tongue twisters has existed for centuries, and likely predates even these early examples. They were probably used for fun, speech practice, and maybe even as riddles or challenges.