I heard viruses and protozoa are spread by contaminated water. Is this true?

Contaminated ? By what? Fecal contamination of water (which is present in all non-treated water) will cause it to contain bacteria and protozoans, both of which can then be transmitted to humans who drink it (e.g., salmonella, giardia). Some of the protozoans at least may carry other organisms (e.g., legionella). Viruses are contained within other cells and could conceivably be carried and transmitted.