Except for yellow fever vaccinations (and that too if you’re coming from a yellow fever zone) the authorities do not require you to have any mandatory immunisations. Furthermore, babies less than a year old need not have yellow fever vaccinations- if, however, there is a risk of infection, they may have to be isolated.
The Philippines is a tropical country, and it has all the diseases common in tropical countries- diseases caused by heat, by humidity and insects. The most common illnesses include malaria, hepatitis, rabies and cholera. Wherever it’s possible, you should get yourself vaccinated beforehand. Where it isn’t possible, take whatever precautions you can- drink only boiled or bottled water, don’t eat anything which isn’t freshly cooked or which you think may not have been cooked with hygiene in mind- and keep clean. Take along insect repellent and malaria pills, as the mosquitoes can be carriers of malaria germs, besides being downright irritating.
On the whole, the Philippines is a fairly safe country to be in- the crime rate isn’t too high, and provided you take a few precautions, you shouldn’t have anything to worry about. Just make sure you don’t leave your valuables lying around, and that should be sufficient. Just one word of caution: take care when travelling between islands- many of them have ferry services going from island to the other, and these ferries are notorious for their high accident rates. Don’t board any ferry which looks rickety or overcrowded- it could be downright dangerous.
On the island of Mindanao, separatist movements have been going on since the last nearly three decades, and there is still some amount of turmoil in the area around Basilan and Sulu, where the government is conducting military operations against the rebels. Should you need to go to these regions, check with your embassy in Manila about the latest situation, and whether it’s safe or not.