We made this transition last summer when my daughter turned 4. She hadn't really been falling asleep very often during nap time, so I told her when she turned 4, she didn't have to nap, but she did have to have quiet time. And here are the rules of quiet time:
1. You must stay in your bed
2. You may have books and quiet toys in your bed
3. You may read, play quietly or sleep.
4. Quiet time is 1 hour long
If she follows the rules of quiet time, she gets to watch a tv show after (that was the incentive for napping prior to that). The funny thing is once we instituted quiet time - she went back to napping most days! Though that only lasted a few weeks, until school started again. But we've had nearly a year of quiet time and it has worked - and mommy has needed it b/c we also have twin 1 year olds - so the rest of us nap while the oldest child is quiet!
Post Script: Now that she's almost 5 she's asking how long she has to have quiet time. I told her once she goes to Kindergarden in the fall she only has to have quiet time on weekends....(LOL only b/c she won't be here!)