My older dd, who will be 5 in September, still naps occasionally; last week we were at the beach and swam and played in the ocean all morning, and stayed up late at night playing games on the boardwalk and getting ice cream, so she napped for at least an hour, sometimes 2, every day. But that's the exception. She stopped napping regularly right around 3, but she was going to p.m. preschool twice a week and that really got her out of the routine. I think she would have continued longer if that hadn't been the case.
I gave up "enforcing" it when it would take her an hour or more to fall asleep each day at naptime, and she was staying up on days she napped until after 9 pm. Some days, I would put her down for nap at 1, and she'd fall asleep at almost 3! Then, she would sleep until I woke her at 4:30 or 5 and bed time would be late in coming. That seemed less than ideal. Now, most days, since she doesn't nap, she's usually asleep before 8 and up at around 7, which gives her the 11 hours of sleep they say is recommended for her age. From time to time when I know she is tired or has a late night ahead of her I will ask her to rest in her bed for awhile; on rare occasions, she will tell me she wants to nap and get into bed and fall asleep!
My younger dd, who will be 3 in October, shows no signs of giving up her daily 2 hour nap. She can miss a nap when I need her to for some reason without completely falling apart, but she tends to make up for it the next day with a longer nap, later morning, etc.