A water faucet or water tap includes, in its base area or other suitable area or region, a built-in or embedded or integrated filtering mechanism. The filtering mechanism includes a non¬ electrical filtering chamber, having a cavity for securing therein a replaceable water-filtering capsule. A suitable water-filtering capsule, having an active filtering component or a passive filtering component, is inserted into the non-electrical filtering chamber, and can be removed from it for periodical replacement. Optionally, the water-filtering capsule includes a scent- producing agent, a flavor-producing agent, or a nutrient or a supplement, which are added to the filtered water. Optionally, a bypass mechanism or water-diverting mechanism enables to select between: a first mode in which a first water-outlet outputs non-filtered mixed hot-and- cold water; and a second mode in which a second water-outlet outputs filtered cold water or filtered room-temperature water.