Is it normal for young children to stop needing naps?

Varies. The need for naps varies considerably across children, along with the overall trend of decreasing need over time. Total sleep over the day is the key. Trouble is those who fight taking naps divide broadly into those who really need one and those who don't. In general, toddlers benefit from an afternoon nap; if it's a struggle, look at ways of making it more routine and less of a battle.