A lot of parents I know see nap time as the most sacred part of their day; it's that break that keeps them sane in the unrelenting job of parenting.
So when your 3-year-old suddenly announces, "I don't want to nap!" and happily makes it through the entire day (with maybe a bit more fuss at supper time), it can bring a full-on state of mourning.
Look at it another way and it can also be freeing - no more rushing home for nap time, trying to keep your child awake in the carseat before you make it home.
How to know it's time to drop the nap
Starting around 3 years old, it's common for kids to no longer need a nap. Some toddlers make the switch a little earlier - they're usually the ones who sleep 12 hours a night and are on the bigger side of the growth curve. On the other end of the spectrum, some kids keep napping well into their fourth year.
You'll know your child is ready when you see signs like:
not being able to fall asleep at nap time, even when you push it later; or
taking for-EVER to fall asleep at bedtime on days when they had a nap.
(Just to be clear, I'm talking about kids who have solid sleep skills and had a regular routine of napping and sleeping through the night.)
Transitioning to no-nap days
If your child is showing one or both of those signs, then I'm sorry to say, your nap-break days are likely over.
Or at least shorter; you can start this transition by capping your child's nap at an hour (ie. wake her up!) if she normally knocks off 2+ hours in the middle of the day. (You may find that when your child first stops napping, he will still fall asleep in the car if you're driving later in the day - when this happens, I would cap the carseat nap at 30 minutes and just push bedtime a half hour later.)
When it's really time to drop the nap altogether, I strongly recommend making Quiet Time the next great thing in your house.
In the beginning, most children struggle to get the concept entirely and, depending on temperament, may even fight it. So you have to make it sound, well... awesome.
How to get your child to love Quiet Time
Tell your child ahead of time that instead of a nap, she can have Quiet Time. Then at lunch time, remind her about the plan:
Start with some dedicated one-on-one time: let your child choose a toy / activity and then spend the next 10 minutes sitting beside her, pretty much doing a play-by-play of her activity. Say things like "You're making the car go round and round!" or "You're making a really tall block tower!" No praise, no direction, no questions. This is the idea behind a miraculous behavioural strategy called "attending". It's kind of like a B12-shot of Mom/Dad attention that can curb your child's need to act out for attention in negative ways (see below for more information on this).
Then read a book (just one!) with your child, have a snuggle, and get him excited about Quiet Time.
Have a few toys / figurines and books in a box that is designated only for Quiet Time. You may have to switch it up or add to this regularly.
Make a simple fort with two chairs and a blanket draped over it with a blanket to sit / lie on inside while he plays. A flashlight can be pretty exciting for a 3- or 4-year-old.
Keep it short in the beginning: about 20 minutes. You want to avoid making your child feel like he’s been banished. You will want a longer break, but you have to take the long view on this: I’m setting you up for years of quiet times!
Give your child choice: “Which of these two toys would you like in your quiet-time fort?” “Would you like the cars or the figurines today?” “You choose three books from this pile.” You have to keep this part quick though.
Give your child a simple kitchen timer, or set the oven timer for 20 minutes; tell him that when it goes off, quiet time is over.
Work up to longer quiet times as your child starts to enjoy it and not protest it.
As soon as your child is contently playing in his Quiet Time spot, go lie down and take your break! It will be over before you know it.
The Attending strategy can be a real miracle for parents struggling with their child's behavioural issues, or just to help build a more positive parent-child relationship. For more information on how to practice Attending, read Parenting the Strong-Willed Child by Rex Forehand and Nicholas Long.