I have been thinking about this question a lot lately- for my 4 year old nephew who doesn’t take naps but falls asleep in any moving vehicle, my son who has dropped a nap and for all of you wondering if your child is getting enough sleep!

Here are a couple of resources on the amount of sleep for certain ages: (keep in mind that a "day" means 24 hours)

This is from WebMD
1-4 Weeks
Old: 15 ½ – 16 ½ hours per day
1-4 Months Old:
14 ½ – 15 ½ hours per day
From 5-8 weeks two hours is about the longest time your baby can stay awake
and remain happy and alert. So he needs to take a nap within that time frame. From 3-4 months old your baby is now getting about two-thirds of sleep at night
with three daytime naps, and so is beginning to establish a more firm day-night
cycle.
4-12 Months
Old: 14 – 15 hours per day
From 4-8 months old, babies typically have three naps and drop to two at around 6
months old…At 9-12 months, your baby now typically sleeps from 10-12 hours at night, takes
two naps, and no longer needs to be fed at night.
   
1-3 Years
Old: 12 – 14 hours per day
As your child moves past the first year toward 18-21 months old
he will lose his morning nap and nap only once a day for an hour and a half to
two hours.
3-6 Years
Old: 10 ¾ – 12 hours per day
Children at this age typically go to bed around 7 – 9 p.m. and
wake up at about 6 – 8 a.m., just as they did when they were younger. At 3,
most children are still napping, while at 5 most are not. Naps gradually become
shorter as well. New sleep problems do not usually develop after 3 years of
age.
7-12 Years
Old: 10 – 11 hours per day
At these ages, with social, school, and family activities,
bedtimes gradually become later and later, with most 12-years-olds going to bed
at about 9 p.m. There is still a wide range of bedtimes, from 7:30 – 10 p.m.,
as well as total sleep times, from 9 – 12 hours, although the average is only 9
½ hours.
12-18 Years
Old: 8 ¼ – 9 ½ hours per day
One study of U.S. high school students found that 13% were
chronically sleep-deprived.

This is from The Sleep Foundation, which the Center for Disease Control recommends as an excellent resource. (They have everything from recognizing potential sleep problems in children, to you, to finding a sleep center and asking an online sleep expert)

Sleep and Newborns (1-2 months)

Newborns sleep a total of 10.5 to 18 hours a day on an irregular schedule with periods of one to three hours spent awake.
Sleep and Infants (3-11 months)
Infants typically sleep 9-12 hours during the night and take 30 minute
to two-hour naps, one to four times a day – fewer as they reach age one.

Sleep and Toddlers (1-3 years)
Toddlers need about 12-14 hours of sleep in a 24-hour period. When they
reach about 18 months of age their naptimes will decrease to once a day
lasting about one to three hours. Naps should not occur too close to
bedtime as they may delay sleep at night.

Sleep and Preschoolers (3-5 years)
Preschoolers typically sleep 11-13 hours each night and most do not nap
after five years of age. As with toddlers, difficulty falling asleep
and waking up during the night are common.

Sleep and School-aged
Children (5-12 years)
Children aged five to 12 need 10-11 hours of sleep. At the same time,
there is an increasing demand on their time from school (e.g.,
homework), sports and other extracurricular and social activities.

Related posts:

1. When Can A Baby Sleep Though the Night?
2. How much sleep at night and how many naps?
3. Adjusting Sleep for Time Zones
4. Time change and sleep
5. Sleep Consultants