The two types of water filters I'd suggest for backpackers are gravity fed or pumps.  The difference is pretty simple, but it's important to understand your environment and what filter will work the best.  Here in the Pacific Northwest, I can easily find streams or deep pools of water deep enough to fill a bottle. 

If, however, you're a desert dweller where water is scarce, you may want to consider a pump.  Pumps have long tubes or straws that you put into the water, then pump it into a bottle.  Once in the bottle the water is purified and ready to drink.  

Most filters these days are pretty incredible and I'd suggest always filtering water to reduce risk of contracting some digestive bacteria lurking in that savory H2O.  

These two filters below are both lightweight, small, and great for one or two people.

 

Squeeze Style or Gravity Fed

  • Sawyer Squeeze

    • The Sawyer Squeeze is a popular options for a lot of folks.  It's small, won't clog easy, and can attach to most any threaded water bottle.  It's good for millions of gallons and all you have to do keep it safe from damage is prevent it from freezing.

Pump Style

  • MSR TrailShot

    • This little guy is impressive.  It's tiny and pumps out water like a champ!  I witnessed it being used on a backpacking trip and was really impressed.  A great option if you're looking for a pump style filter.