Countertop Water Filters

1.   The first method hooks up to the end of your kitchen tap to supply unlimited amounts of filtered water on demand.
See the MAX Stainless Steel Countertop Filter or the CB Tech Stainless Steel Countertop Filter.
2.   The second method works by gravity. You manually fill an upper reservoir (which contains filters) with water and let gravity filter the water into the lower receiving tank.
See British Berkefeld Gravity Filter Systems and Portable Gravity Filters. 
3.   The third type of countertop filter requires electricity, is filled manually, is relatively portable, and delivers purified water.
See the AquaTru Countertop Water Purifiers.