What types of infections can I get from contaminated drinking water?

Waterborne illnesses. You can get infections which are passed via the fecal oral route such as giardia, cryptosporidium, hepatits A, norovirus, camplobacter, Salmonella, and E. Coli most of which cause gastroenteritis with diarrhea and cramping. http://www.cdc.gov/healthywater/drinking/public/water_diseases.html.
Multiple. possibilities: bacteria infection or amebic infection of the stomach and intestines, fungal infections and sepsis.
Many. Many infections but generally those related to protozoa (such as amebiasis, cryptosporidiosis, giardiasis, microsporidiosis), parasites (such as schistosomiasis, teniasis, ascariasis, enterobiasis), bacteria (such as cholera, botulism, E. coli infections, dysentry, typhoid, salmonellosis) and viral (such as polio and hepatitis).