Rotavirus, Pertussis, and invasive disease due to hib and penumoccocal bacterias are probably the ones that are most pressing for an infant-3 year old. You can attempt to "hide in the herd" with hib and PCV diseases as their numbers have dropped a lot due to vaccination, but both can be very risky if caught. hib in particular is troublesome, with high rates of death and long term health risks due to meningitis, epiglotitis, pneumonia, etc. Pneumoccocal diseases are more common that hib infection; there are many strains and the PCV 13 vaccine is recommended over the PCV 7 if you are looking for protection from the worst and most common strains.
Pertussis is definitely out there and can be caught both if vaccinated and if not; however, if you do become symptomatic and are vaccinated, the disease severity is definitely a lot less...think a week or so of a cold/cough vs weeks to a month or more of coughing spelling, of puking while coughing, pneumonia risks, etc.
The rotavirus vaccine is pretty effective and has drastically cut down the hospitalization rates due to the disease. It is another one that is quite common under the age of 5 (and many studies suggest we pretty much all get it with varying degrees of symptoms by the time we are 5). Breastfeeding is protective and helpful with symptoms, though the disease can still be serious to breastfed infants (I can show you some case studies if you want but I think you get the idea). It's a risk/benefit decision you have to make when it comes to vaccines. this vaccine can cause mild rota-like symptoms.
MMR is not given to infants, so really that one doesn't come into the picture until a year or later. It's more effective if given later anyway (15-18 months, for example, gives better immunity than 12 months).
IPV is one you won't really have risk for in the USA. Other parts of the world, such as russia, have seen the disease reintroduced through travel but so far the USA has not run into this.
Hep B is spread by bodily fluid contact with an infected person. rarely it can be spread by biting and even spit (some recorded cases of spit in the eye transmission). but unless you have a positive family member or your children will spend a lot of time in care outside the home, the risks are really really low (and even with day care it is still low though transmission for kids in that situation is slightly higher than at home).
I believe, the bottom line, is that you do have a higher risk of most VPDs if you do not vaccinate but you have to make the risk/ benefit analysis on your own and go from there.
"Parents are simply trustees; they do not own the bodies of their children"-Norm Cohen Martial arts instructor and mom to 4: DD1 (1/05) DS (7/06) DD2 (5/08) DD3 (2/11)