When should my child stop napping?

It depends. Every child is different; some kids go to 1 nap daily at 1 year old, others not til 2 years. Some kids give up napping completely at 2, others still nap at 8. Some adults even benefit from a nap! if your toddler no longer falls asleep at nap time, yet seems to still be cheerful and active all day, then no naps are needed.
It depends. Each child is different, some children stop napping earlier than 2 and some continue to nap until school age. Each child whether they nap or not should have some quiet time. So if your child is resisting naps, try some quiet play or quiet time instead.