What are the corresponding titles for "Dr." (in the sense of MD and PhD) in Chinese?
All the information is taken straight from Wiktionary's English entries and the Chinese/Mandarin translations thereof. You don't really need to know any Chinese to find the information:

Doctor (physician): 医生, 大夫.
Doctor (person with a doctorate): 博士
Doctor (vet): 兽医

Doctor of Philosophy: 哲学博士 

Graduate (from a university): 毕业生


博士 can be used as a title. For example you'd call me 焦博士 if I was an academic doctor (I wish). 

毕业生 is usually used without a name attached; however, if you have to use it as a title (which is really unusual in either English or Chinese), then you can append the name of the person at the end of it: 毕业生James or 毕业生小焦.