If most cases, you do not need a vaccination for entering Singapore. The only instance you would need a vaccination is if you were in a country where yellow fever is endemic up to six days before you arrive in Singapore.
Hepatitis A and B are prevalent in Singapore, so you might want to get a hepatitis jab before coming. The country does suffer from dengue fever epidemics from time to time, but there is no vaccine for that - you just have to take care about mosquito bites and use necessary repellants.
Getting travel insurance would be advisable, so that if you should fall sick, your insurance can pay for medical services in Singapore.
Dear visitor, thank you so much for reading this page. My name is Timothy Tye and my hobby is to find out about places, write about them and share the information with you on this website. I have been writing this site since 5 January 2003. Originally (from 2003 until 2009, the site was called AsiaExplorers. I changed the name to Penang Travel Tips in 2009, even though I describe more than just Penang but everywhere I go (I often need to tell people that "Penang Travel Tips" is not just information about Penang, but information written in Penang), especially places in Malaysia and Singapore, and in all the years since 2003, I have described over 20,000 places.
While I try my best to provide you information as accurate as I can get it to be, I do apologize for any errors and for outdated information which I am unaware. Nevertheless, I hope that what I have described here will be useful to you.