When do kids stop napping?

I need advice on naps. My son is 2.5 and just transitioned from the crib to a big boy race car bed (twin size). He always cried in the crib to take naps but would lay down in a few minutes and go to sleep. Now that he has a big bed and knows he can get up, naps have been nonexistent. He either lays there talking to himself, or he gets up and plays. Should I even try to lay him down during the day? Yesterday, he woke up around 9 am went all day with no nap, and by 9 pm, he was fed dinner, had a bath, and fell asleep and slept all night till 930am today. Is that bad? I kind of like putting him to bed earlier than trying to force a nap during the day. Or should I take it day by day? Help!