Why do we have more male infants born?
Note: This is based on literature searches I've done a while ago out of general curiosity. I'm in no way an expert on human reproduction.



First, I'm not sure if you are asking about evolutionary reasons or the  developmental causes for for a difference in sex ratio. Here, I will focus on the developmental causes.

There is much evidence for a male bias in human sex ratio at birth (secondary sex ratio), and the ratio have been shown to change over time, e.g. as in 20th centrury Europe after WWI and WWII (see data in Gellatly, 2009),in relation to environmental or parental factors (see e.g. Jacobsen et al, 1999), or between ethnic groups.

A bias in sex ratio can be due to (at least) three different mechanisms (Irving et al (1999)):


deviations in X/Y-ratio of sperm
selection of sperm within the female reproductive tract
biases in implantation success and/or survival for embryos of different sex


I guess that success of fertilization/zygote formation could maybe be considered a separate step (between 2-3). From what I've seen, there is little evidence for explanation one, see tests in e.g. Irving et al (1999) and Graffelman et al (1999). Graffelman et al (1999) also tests for an effect of male age, but do not find support for this idea. 

A problem is that it is extremely difficult to study these factors under natural conditions (practically and ethically). Interestingely, there is also evidence for an excess loss of male fetuses in recognized pregnancies (Ingmarsson, 2003, Boklage, 2005), and this would indicate that the sex ratio close to conception is even more skewed towards males than the sex ratio at birth. This is even more curious with the background of an unbiased sex ratio in sperm (explanation 1 above). However, it is very problematic to study what happens in the first part of pregnancies, since a number of weeks have usually passed before the pregnancy is even recognized. I haven't found any papers reporting the human primary sex ratio (sex ratio at conception), which could be affected by factor 1 &amp; 2 above.

Even so, the most likely explanation seems to be a strong bias during embryogenesis, as mentioned in Boklage (2005): 


  The usual excess of males is present through pregnancy beyond clinical recognition, but not present at fertilization. The difference, therefore, must arise between fertilization and clinical recognition, through a preferential loss of females during embryogenesis. 


The same paper also points out that fewer than 25% of natural human fertilizations go full term (probably even less), and 2/3 of these fail before the pregnancies have been clinically recognized. By back-calculating from the secondary sex ratio and the excess of failed male pregnancies, the sex ratio close to conception has been estimated to 125-135 male:100 female (Pergament et al, 2002))

The exact causes for such a bias during is not entirely known from what I've seen. However, Boklage (2005) mentions a couple of different explanations. For instance, among mammals in general, the earliest stages of embryogenesis proceeds more rapidly in male embryos:


  Since some of the products of these earliest stages are signals from one part of the embryo to another, or from the embryo to the maternal physiology, signals which are required for continuation and maintenance of the pregnancy, the establishment of viable, clinically recognizable pregnancy is correspondingly more efficient in general for male embryos (Krackow, 1995; Kochhar et al., 2003). 


The same issue is also mentioned in Ingvarsson (2003):


  Studies in recent years indicate that sex differentiation begins at conception. The SRY gene on the Y-chromosome is already transcribed at the 2-cell stage and triggers growth acceleration in the XY embryos. This accelerated growth is believed to be important for the male embryo as it allows complete testicular differentiation before the levels of oestrogenic hormones become too high as pregnancy progresses.


Boklage (2005) also mentions genomic imprinting and chromosome X–Y segregation as possible explanations for a bias (see references in paper for more).

So, in summary; there is evidence for an male bias in secondary sex ratio (sex ratio at birth), even though there is usually a excess of failed male fetuses in recognized pregnancies, which means that the male bias must be even higher very early in pregnancies. There is some evidence that this might be due to a higher success of embryogenesis of male fetuses, but the evidence isn't strong and the issue is difficult to study.


  The evidence provided by these results is indirect. That is unlikely to change. Ethical, technical and financial considerations argue against the destruction for karyotyping of statistically sufficient numbers of products of natural human fertilizations. Granted, any bias of the sort we seek to discover and understand might, after all, operate differently, or not at all, in sham fertilizations of hamster oocytes, versus oocytes from artificially induced human ovulations, versus naturally fertilized human oocytes. The best evidence we have, or are likely to have in the foreseeable future, indicates that the consistent excess of males observed in human births does not originate in a consistent bias in spermatogenesis or in fertilization. 
  (Boklage, 2005)


Finally, it should also be mentioned that the bias in sex ratio at birth can be partially due to sex-selective abortion and infanticide, but to what extent is not entirely known (see Wikipedia: Sex-selective abortion).

You might also find this related question on the heritability of sex ratio interesting: The gender of offspring of Twins?.