The accepted answer doesn't really answer the question (are men smarter than women), but a different question (did Scottish boys in 1932 perform better on an IQ test than girls).
The conclusion that is drawn is disputed by newer research. Researchers who think that men have a higher IQ argue that this discrepancy doesn't happen until 15 (although that fact is obviously disputed by researchers who do not think that there is a sex difference above age 15).
I don't have a definitive answer to the question, but I will try to give an overview over existing studies on the topic.
Studies arguing that men are smarter than women
The main proponent of the idea that men are smarter than women is Richard Lynn, whose work on intelligence has been severely criticized as biased, racist, and disregarding scientific objectivity.
In 1998 Lynn looked at sex differences in Scotland:
In a Scottish standardisation sample of the Wechsler Adult Intelligence Scale-Revised, men have a mean IQ of 105.09 and women of 100.00. The higher average mean obtained by men is consistent with four other standardisation samples of the WAIS and WAIS-R.Lynn, 1998. Sex differences in intelligence: data from a Scottish standardisation of the WAIS-R
An article from 1999 looked at sex differences in Estonia:
1201 applicants for entry to the University of Tartu were given tests of verbal, reasoning and spatial abilities and of scholastic knowledge. Males scored significantly higher than females on all four tests and on the g factor. The male advantage is estimated at 6.6 IQ points.Allik, Must & Lynn, 1999. Sex differences in general intelligence among high school graduates: Some results from Estonia
A study from 2002 looked at differences in development:
The general trend shows that girls do better at the younger ages and their performance declines relative to boys among older age groups, which supports the developmental theory. The sex difference for the DAT as a whole for 18 year olds is a 4.3 IQ advantage for boys, very close to the advantage that can be predicted from their larger brain size (4.4 IQ points). Lynn & Colom, 2003. Testing the developmental theory of sex differences in intelligence on 12–18 year olds
A study from 2003 looked at data from Hong Kong:
The results are that males obtained a higher mean score than females of 1.6 raw score points, equivalent to an advantage of 3.2 or 4.1 IQ points, according to two alternative methods of calculation. Lynn & Tse-Chan, 2003. Sex differences on the progressive matrices: some data from Hong Kong.
A study from 2004 looking at data from New Zealand:
Sex differences on the WISC-R were examined in a sample of 897 New Zealand children studied at ages 8 and 9 years. Boys scored significantly higher than girls on the subtests of information, vocabulary, block design and object assembly, while girls scored significantly higher on coding. Boys obtained slightly but not significantly higher scores on the verbal, performance and full scale IQs. Lynn, Fergusson & Horwood, 2004. Sex differences on the WISC-R in New Zealand
Data from 2005 from Mauritius:
Sex differences on the WISC-R (Wechsler Intelligence Scale for Children-Revised) are examined in a sample of 1258 11 year olds in Mauritius. Boys obtained a significantly higher Full Scale IQ by 5.8 IQ points. Boys obtained a higher Performance IQ by 6.5 IQ points and a higher Verbal IQ by 1.0 IQ points.Lynn et al, 2005. Sex differences on the WISC-R in Mauritius
In 2004, Lynn and Irwing did a meta-analysis:
A meta-analysis is presented of 57 studies of sex differences in general population samples on the Standard and Advanced Progressive Matrices (SPM and APM, respectively). Results showed that there is no difference among children aged 6–14 years, but that males obtain higher means from the age of 15 through to old age. Among adults, the male advantage is 0.33 d equivalent to 5 IQ points. Irwing & Lynn, 2004. Sex differences on the progressive matrices: A meta-analysis
In 2005, Lynn and Irwing did a meta-analysis of various studies. Their conclusion is that there is not a greater variability in men, but that men are smarter on average:
A meta-analysis is presented of 22 studies of sex differences in university students of means and variances on the Progressive Matrices. The results disconfirm the frequent assertion that there is no sex difference in the mean but that males have greater variability. To the contrary, the results showed that males obtained a higher mean than females by between .22d and .33d, the equivalent of 3.3 and 5.0 IQ conventional points, respectively. Irwing & Lynn, 2005. Sex differences in means and variability on the progressive matrices in university students: A meta-analysis
The methodology they used has been criticized by Blinkhorn in Nature, especially for excluding a study from Mexico. Lynn and Irwing rejected the criticism.
A study by Nyborg from 2003 finds a sex difference in intelligence and tries to explain why other studies don't:
The present study addressed this paradox by testing four hypotheses: (1) Inadequate analyses explain why researchers get inconsistent results, (2) The proper method will identify a male g lead, (3) The larger male brain “explains” the male g lead, (4) The higher male g average and wider distribution transform into an exponentially increased male–female ratio at the high end of the g distribution, and this largely explains male dominance in society. All four hypotheses obtained supportNyborg, 2003. Sex-related differences in general intelligence g, brain size, and social status
A study by Jackson and Rushton finds differences:
In this study we found that 17- to 18-year old males averaged 3.63 IQ points higher than did their female counterparts on the 1991 Scholastic Assessment Test (SAT).Jackson & Rushton, 2005. Males have greater g: Sex differences in general mental ability from 100,000 17- to 18-year-olds on the Scholastic Assessment Test
Studies arguing that there is no (or negligible) sex difference in intelligence
A study by Colom et al from 2000:
Cognitive batteries were applied in the present study to independent samples totaling 10,475 adult subjects (4,256 females and 6,219 males). The scores were factor analyzed by sex to obtain separate g factors. [...] The results suggest a negligible sex difference in g.Colom et al, 2000. Negligible Sex Differences in
A study by Flynn and Rossi-Case from 2010:
Raven’s Progressive Matrices data of high quality from five advanced nations show that females matched males both below and above the age of 14. This counts against hypotheses that genetic factors cause general intelligence differences between the genders. Flynn & Rossi-Case, 2010. Modern women match men on Raven’s Progressive Matrices
A study by Savage-McGlynn from 2011 disputing the Developmental Theory of Sex developed by Lynn (the idea that men develop slower, but have a higher intelligence after the age of 15):
Using a nationally representative sample of children, multiple-group confirmatory factor analyses have been used to assess mean differences in younger (7–14 years) and older (15–18 years) groups. No significant differences were found in mean performance or score variance, failing to provide evidence for a Developmental Theory of Sex Differences in general intelligence.Savage-McGlyn, 2011. Sex differences in intelligence in younger and older participants of the Raven’s Standard Progressive Matr
A study by Camarata and Woodcock finds:
There was a high degree of concordance across tests and no sex difference was observed in overall estimates of general intellectual ability (GIA) on the WJ III.Camarata & Woodcock, 2006. Sex differences in processing speed: Developmental effects in males and females
Studies finding that there is a sex difference in favor of women
A study by Keth et al disputes the Developmental Theory of Sex:
The higher-order, latent g factor showed inconsistent differences for children, small, non-significant differences favoring females for adolescents, and fairly consistent statistically significant differences favoring females in adulthood. Findings are inconsistent with developmental theory that suggests males should show an advantage on g in adulthood. Keith et al, 2008. Sex differences in latent cognitive abilities ages 6 to 59: Evidence from the Woodcock–Johnson III tests of cognitive abilities
Studies finding higher variance among men
There are studies that suggest that there is no difference in the mean, but that there is a greater variance among men. For example:
Males have only a marginal advantage in mean levels of g (less than 7% of a standard deviation) from the ASVAB and AFQT, but substantially greater variance. Among the top 2% AFQT scores, there were almost twice as many males as females.Irwing et al, 2006. Brother–sister differences in the g factor in intelligence: Analysis of full, opposite-sex siblings from the NLSY1979
This may not be satisfactory, but there is no definite answer as intelligence is a complex topic. Wikipedia provides a good overview though:
Differences in intelligence have long been a topic of debate among researchers and scholars. With the advent of the concept of g or general intelligence, many researchers demonstrated no significant sex differences in g factor or general intelligence while others have argued for greater intelligence for males. The split view between these researchers depended on the methodology and tests they used for their claims. One study did find some advantage for women in later life, while another found that male advantages on some cognitive tests are minimized when controlling for socioeconomic factors.