According to the Ministry of Health as of 2015 there are 16 public hospitals and specialty centres in SIngapore.
SingHealth (https://www.singhealth.com.sg/) provides public services in the eastern part of singapore and the National Healthcare Group (https://corp.nhg.com.sg/) in the west. The National University Health System (http://www.nuhs.edu.sg/) is the third public healthcare provider.
You can read more about Singapore's hospitals on the Ministry of Health website (https://www.moh.gov.sg/content/moh_web/home/our_healthcare_system/Healthcare_Services/Hospitals.html)
Public hospitals include:
Some restructured facilities focus on specific ailments, for example the
National Cancer Center tel +65 6236 9433 email fps@nccs.com.sg
National Dental Center tel +65 6324 2215 email appointment@ndc.com.sg
National Heart Center tel +65 6844 9000 email ims@nhcs.com.sg
National Neuroscience Institute tel +65 8128 8007 email nni_secretariat@nni.com.sg
Singapore National Eye Centre tel +65 6100 9393 email ips@snec.com.sg