For the Boundary Waters area, though, I'd go both the pump and chemical route. Not that there's anything unusually dangerous about the water there, but giardia is certainly an issue, and in still waters I'd also be mildly concerned about viruses.
So my first choice would be a pump such as an MSR MiniWorks EX ($79; www.msrcorp.com) or a Katadyn Hiker Microfilter ($60; www.katadyn.com). Both will remove bacteria and parasites such as giardia, while also neutralizing any off tastes from the water (the Katadyn does the latter with an activated charcoal core; the EX uses a ceramic/carbon core).
Then I'd go an extra step and use MSR's SweetWater Purifier Solution ($9). Add a few drops to your filtered water, wait five minutes, and drink. It uses a chlorine solution that kills just about any virus found on the planetnetting those nasties that filters can't catch.
For the final word on water purification, read "Die, Bugs, Die!" from Outside's 2004 Buyer's Guide.