Yes, fluoridated water works to reduce dental caries in children.
This answer originally consisted of one study based in the USA. This was revealed to be insufficient by a significant edit to @Skeptic's answer, which contained eight similar studies from different regions, drawing different results.
In such situations, where there are conflicting studies, there is a risk of cherry-picking. (In my case, the study was found by working backwards from the WHO report on fluoridation.) It becomes important to look not at individual studies or even who can produce the most studies, but at a systematic review of all of the studies, based on their quality and statistical power. Below, I repeat the original study I quoted, for completeness. Then, I look at a more powerful meta-analysis of the data.
This study looked at the results of two large epidemiological surveys:
DMFS (Decayed/Missing/Filled Surface) is a measure of tooth-decay used in dentistry. They found that children who grew up in fluoridated areas had 18% lower DMFS scores than those who never lived in fluoridated areas. If you removed the impact of other sources of fluoride, this jumped to 25%.
The decline in dental caries in US schoolchildren, first observed nationwide in 1979-1980, was confirmed further by a second national epidemiological survey completed in 1987. Mean DMFS scores in persons aged 5-17 years had decreased about 36% during the interval, and, in 1987, approximately 50% of children were caries-free in the permanent dentition. Children who had always been exposed to community water fluoridation had mean DMFS scores about 18% lower than those who had never lived in fluoridated communities. When some of the "background" effect of topical fluoride was controlled, this difference increased to 25%. The results suggest that water fluoridation has played a dominant role in the decline in caries and must continue to be a major prevention methodology.
Again the above study should be treated with care, as there are conflicting studies. Instead, we should look at the preponderance of evidence with a meta-analysis:
- Marian S McDonagh, Penny F Whiting, Paul M Wilson, Alex J Sutton, Ivor Chestnutt, Jan Cooper, Kate Misso, Matthew Bradley, Elizabeth Treasure and Jos Kleijnen. Systematic review of water fluoridation BMJ. 2000; 321(7265): 855–859. PMCID: PMC27492
In this systematic review, a total of 214 studies were incorporated.
45 controlled before-after studies, 102 cross sectional studies, 47 ecological studies, 13 cohort (prospective or retrospective) studies, and seven case-control studies
Each of the studies was considered "low to moderate" quality, so the existence of conflicting results is not too surprising.
Of those 214, 26 were related to the key question here - water fluoridation and dental caries.
They found that fluoride helps with caries:
Water fluoridation was associated with an increased proportion of children without caries and a reduction in the number of teeth affected by caries. The range (median) of mean differences in the proportion of children without caries was -5.0% to 64% (14.6%). The range (median) of mean change in decayed, missing, and filled primary/permanent teeth was 0.5 to 4.4 (2.25) teeth.
One of the figures gives a visual representation of the variance in the results:

They also found there were the expected minor side-effects - fluorosis:
A dose-dependent increase in dental fluorosis was found. At a fluoride level of 1 ppm an estimated 12.5% (95% confidence interval 7.0% to 21.5%) of exposed people would have fluorosis that they would find aesthetically concerning.
I have included three more studies which are of related interest:
The existing body of evidence strongly suggests that water fluoridation is beneficial at reducing
dental caries. After adjustment for potential confounding variables, McDonagh et al (2000a) showed
in their systematic review that the introduction of water fluoridation into an area significantly
increased the proportion of caries-free children, and decreased mean dmft/DMFT scores compared
with areas which were non-fluoridated over the same time period. The findings of McDonagh et al
(2000a) also suggest that cessation of fluoridation resulting in a narrowing of the difference in caries
prevalence between the fluoridated and non-fluoridated populations. Only one additional relevant
original study was identified in the current review and this did not change the conclusion of the
existing systematic review.
(This also addresses an earlier discussion point that I didn't know what dose of fluoride I had swallowed today, by showing the model used to calculate it when determining the appropriate fluoridation levels in my country.)
Our review found that water fluoridation is effective at reducing levels of tooth decay among children. The introduction of water fluoridation resulted in children having 35% fewer decayed, missing and filled baby teeth and 26% fewer decayed, missing and filled permanent teeth. We also found that fluoridation led to a 15% increase in children with no decay in their baby teeth and a 14% increase in children with no decay in their permanent teeth.