It's technically correct to add the dot, I do, though colloquially many people leave it out. And interestingly people will actually start pronouncing it that way as well, you'll often hear zindagi incorrectly said as jindagi, not even just spelled that way, spoken. Strange phenomenon. I would include the dot when you type though, it's more correct
Generally (perhaps always, not sure) words with ज़, ख़, etc. are from Persian, and sometimes have a secondary etymology from Sanskrit (i.e. they are 'doublets') without the dot.
I understand preference between the two is thus essentially regional, and spills over into other words similar sounds to which that etymologyical reason doesn't actually apply, so you get mixed pronunciation like sabji & sabzi.