Here is a pretty extensive overview of various water treatment options and real-life application:
http://www.ianrpubs.unl.edu/epublic/live/ec703/build/ec703.pdf

Sounds like in many cases at least a two-stage process would be needed to purify heavily contaminated water. Also, each treatment method has various practical limtiations. For example, an activated carbon filter is effective at removing many organic compounds, but only as long as its capacity isn't exceeded. Once that happens, the filter will no longer work and may in fact begin to release the previously accumulated contaminants back into the water.