Bog Water can only be found in Swamplands as for now.
Currently (April 2017) Bog Water is not poisonous for player-characters to swim in (or rather wade in, as it usually is only 1 block deep, except for parts where it might flow down into caves).
While staying in Bog Water (if a sufficient amount of Bog Water is around) the air above appears greenish and foggy.
Reeds, Cattails and Lilypads can often be found in Bog Water in "naturally" generated Swamplands, however no more of these seem to spawn in Bog Water over time. Some of these plants can be used as a Fuel in the Forge as well as for decoration purposes, but none of those are necessary ingredients in any crafting recipes as of yet (April 2017).
You can use Bog Water to water Crops by placing it next to tilled land, but by using too much Bog Water a whole area could be made infertile, just like Swampland biomes let Seeds and Queen Bees stay fallow.
Bog Water can freeze nearly as easily as ordinary Water. When throwing Fire Bombs at Bog Water, the greenish liquid will evaporate, leaving nothing behind. However Bog Water is non-flammable otherwise, so simple Torches cannot set Bog Water ablaze, and it does not really burn or even spread fire further, unlike Tar.
Bog Water can be put to display in Wood Planters, Flower Pots, Placemats,Hidden Temple Altars and on Wall Shelves, but is not always displayed in/on all of these objects visibly in 3D (as of April 2017).