Lots of input already. I'll add my two cents:

Chemical treatment

• Iodine--works against bacteria and viruses, not against cysts.
• Chlorine dioxide (ClO2)--several log more effective than iodine against bacteria, effective against giardia in 30 minutes, 4 hours for crypto.
• Miox (mixed oxidizers)--brews up a mix of free chlorine, ClO2, hypochlorous acid and trace amounts of other oxidizers. Same general effectiveness as ClO2, in my experience tastes rather stronger (probably varies depending on source water and one's palate sensitivity).
• Household bleach (sodium hypochlorite)--A little better than iodine against cysts, less effective against bacteria and viruses than ClO2. Basically free.

I don't like chemical treatments for aesthetic (taste and odor) reasons and their spotty efficacy. ClO2 tablets are the simplest and probably affect water taste the least, so that's my standard fallback in case my primary method fails, or I'm day hiking. Over the long haul, it's a very expensive option (the two-part liquids are much cheaper than the tablets). All the tablets are made by the same company but are packaged by a few for retail sale.

I will never rely on iodine or household bleach, period; virtually every other chemical option has much better results. Miox is fun to fiddle with, but tastes like a salty swimming pool.

UV

Broadly effective against viruses, bacteria, cysts. Affected by turbidity and temperature (device design can counteract the temperature effect to some extent). Instant (stir and drink) and does not affect taste. It's fine for soloing, but IMHO too fiddly for groups (far too much scooping, stirring and pouring). Batteries are an ongoing cost and don't be tempted by cheap offbrand CR123s.

Filtration

The most common tool. I've used many, many over the years and so long as I'm not fixated on viruses (I'm not) does what I need w/o affecting taste. After years of pumps I've converted to gravity filtration. Because I'm lazy. I won't go into comparatives among brands and models, I've settled on the Sawyer system. It flat works and with adequate backflushing is a lifetime purchase. They do make a virus-level filter with a rather lower flow rate. If I were headed to the tropics I'd get that.

Drink up!