It depends on the level of protection you're seeking; following filtration with certain chemical treatments gets more "bad stuff" than filtration alone.

It's important to understand the differences in effectiveness between chemical-only, filter-only, purifier-only, or some combination of mechanical-and-chemical; and now, as Brangdon mentioned, ultraviolet purifiers like the AquaStar (or the SteriPEN).

Once you're familiar with the results each process will yield, then you have to decide what level of protection you're comfortable with. Want to avoid exposure to waterborne viruses? Then filter-only treatment is not for you. If usage will mostly be in remote backcountry, maybe you'd be comfortable with filter-only. Conversely, if expected usage will be nearer urban areas, I'd personally want my drinking water purified, and not merely filtered.

Again, for a thorough discussion of water treatment processes/equipment, I recommend the REI article.