Why does my 3 year old toddler's bottom always itch? Sometimes he also says it hurts. There is no rash or other visible signs. What could it be?

Bottom line:further. There is a list of possibilities why your son's bottom may itch. We would need to know where (buttocks vs. Near the rectal area) use of topical creams/soaps, redness, stooling patterns and appearance, and any additional overall body signs and symptoms. Pain adds an additional dimension which requires further questioning. Bottom line: further evaluation required.
Could be pin worms. I would say get him checked. Pinworms commonly cause rectal itching in young children.