Just because something was advantageous from an evolutionary standpoint at one time, doesn't mean that it continues to be the case later.
IOW, it can be argued that we're now more than a bag of [link|http://en.wikipedia.org/wiki/The_Selfish_Gene|selfish genes], but one can also argue the other way:
Dawkins proposes that genes that help the organism, which they happen to be in, to survive and reproduce tend to also improve their own chances of being passed on, so \ufffd most of the time \ufffd "successful" genes will also be beneficial to the organism. An example of this might be a gene that protects the organism against a disease, which helps the gene spread and also helps the organism. There are other times when the implicit interests of the vehicle and replicator are in conflict, such as the genes behind certain male spiders' instinctive mating behaviour, which increase the organism's inclusive fitness by allowing it to reproduce, but shorten its life by exposing it to the risk of being eaten by the cannibalistic female. Another good example is the existence of segregation distortion genes that are detrimental to their host but nonetheless propagate themselves at its expense. Likewise, the existence of junk DNA that provides no benefit to its host, once a puzzle, can be more easily explained. A more controversial example is aging, in which an old organism's death makes room for its offspring, benefiting its genes at the cost of the organism.
These examples might suggest that there is a power-struggle between genes and their host. In fact, the claim is that there isn't much of a struggle because the genes usually win without a fight. Only if the organism becomes intelligent enough to understand its own interests, as distinct from those of its genes, can there be true conflict. An example of this would be a person deciding not to breed because they'd be miserable raising children, even though their genes lose out due to this decision.
When looked at from the point of view of gene selection, many biological phenomena that, in prior models, were difficult to explain become easier to understand. In particular, phenomena such as kin selection and eusociality, where organisms act altruistically, against their individual interests (in the sense of health, safety or personal reproduction) to help related organisms reproduce, can be explained as genes helping copies of themselves in other bodies to replicate. Interestingly, the "selfish" actions of genes lead to unselfish actions by organisms.
Prior to the 1960s, it was common for such behaviour to be explained in terms of group selection, where the benefits to the organism or even population were supposed to account for the popularity of the genes responsible for the tendency towards that behaviour. This was shown not to be an evolutionarily stable strategy, in that it would only take a single individual with a tendency towards more selfish behaviour to undermine a population otherwise filled only with the gene for altruism towards non-kin.
I haven't read the book, but what I know of it makes some sense but also strikes me as assigning a little too much volition to bits of DNA. While biology certainly works to have fitter genes survive, at the level of individuals much more comes into play (good and bad choices, good and bad luck, emotions, etc., etc.).
Most of us consciously worry much more about our immediate families than about cousins or aunts and uncles that may share a great many genes with us. I worry much more about my step mother (who I likely share few familial genes with) than I do about my cousins (who I haven't seen in decades). Since I won't be having any children, it's rather academic, but I think I'm not that much of an outlier in regarding personal closeness as being more important than shared genes. So I think replication of familial genes was once a much stronger imperative than it is now; witness the story of [link|http://www.biblegateway.com/passage/?search=Genesis%2038:8-10;&version=31;|Onan]. Sex has much more to do with things other than reproduction these days. Parachute jumping, or eating lots of sugar, or driving fast feels good, but it's hard to argue that it's a beneficial evolutionary strategy these days. :-)
My $0.02.
Cheers,
Scott.