This is a hard question to answer, the following are just some of my random thoughts.
Fisrtly there are no perfect vaccines. It is almost impossible to produce a vaccine that gives 100% protection with zero risk. The risk or a vaccine is always balanced against the risk of the disease. However the vaccines around now are much safer than examples from the past and carry extremly low risks.
Many vaccines seem unnessesary now only because almost everyone in the population is vaccinated. Most serious childhood diseases are largely forgotten in Europe and the USA but have not gone away and are only a flight away. If vaccination rates drop below a critical level, usually about 80%, these epidemic diseases are soon back. Measles still kill hundreds of thousands of unvaccinated children worldwide each year. Not vaccinating and relying on the protection of everyone else vaccinating is very selfish. There are children and adults who cannot be vaccinated for various reasons and they rely on the protection from everyone else who is.
The idea vaccinating babies or multiple vaccinations is harmful: Vaccines produce a very small immune response compared to the real infection. Babies are exposed to hundreds of bacteria and viruses from imediatly after birth, they are everywhere and were far more so in our evolutionary history. Response of the immune system to mutiple potential threats at once at a very young age is completely natural, it is what the immune system is designed to do. A babies immune system is identifying, responding to and fighting off many threats everyday. Many vaccines are given very early because it is ofen the young children that are most at risk of dying from viral infections like measles.
Most childhood vaccines given now target viral infections. These are viral diseases spread from person to person and for which there is little effective treatment. These diseases have little to do with good sanitation, clean water or good diet. While the rational for vaccinating against childhood diseases is obvious, some others like Hepititis B are less so. Population wide vaccination often involves a pragmatic approch. Most people will simply never come back for vaccinations as a teenager or adult. Also the people who will most need it are probably the least likely to get it as an adult.
People who work in public health to prevent infectious diseases are usually good people who want to make the world a better place and usually don't get paid a great deal for doing it. I would not compare it to nutritional science. With a disease like measles you know if what you do works, either people get measles or they don't. It's not like trying to work out how diet affects heart disease. As an aside, the guy who developed the Hepititis B vaccine worked at my University http://www.research-innovation.ed.ac.uk/success/hepatitisB.asp he gave away all the royalties he would have made from the vaccine.
And finally a song http://www.youtube.com/watch?v=u1xw0Ob5bqs&feature=player_embedded
The CDC has alot of very good information on vaccines such as the long answer, reccommeded child vaccination scedule.
There is information on each vaccine preventable disease.
I feel strongly about think there are reasonable arguments that these vaccines given to children. Some are to prevent common dangerous diseases. Some to prevent diseases re-entering the issueUSA like polio. Others to reduce the longer-term risks the child like hepatitis. I think the common childhood diseases are the most important to vaccinate very young children against.