We often hear about about how chimpanzees are our closest genetic relatives, but what about the other side of the scale? Which species is humanity’s most distant cousin?
The Klingons.
Probably flowering plants, given you’d have to go all the way up the evolutionary tree to the most primitive organisms, the archaea, before the animal / plant split, and back down.
So that’s why the never send Christmas cards. 
No, no, no. You and I, the General Sherman Tree, Meeb the amoeba, and that mushroom over there, are all members in good standing of the Eukaryotes. The Moneran bacteria and cyanophytes and the Archaeans don’t even have the same sort of cells as we do. Almost certainly an archaean of some sort is much more distantly related than an any eukaryote.
I originally thought that, but then I remembered that you have to count the steps both directions, both up and down. So archaea would be more closely related, as you’ve only got the steps up.
The OP specified “genetic” distance, not “number of steps”. (Not really sure what you mean by that, but it doesn’t matter.)
What makes you think bacteria and archae haven’t been evolving every bit as much as we have?
I can’t speak about bacteria, but a few moments thought about Archaea should give you a clue that they haven’t significantly evolved.
Why? Archea are evolving just like everything else. In genetic terms, archea and eubacteria are probably evolving faster than big animals like us. They’ve got greater mutation rates and much faster generation times. There are probably modern archea species that are radically different from their ancestors.
We can’t call an organism “less evolved” with any sort of scientific accuracy simply because they retain a superficial sort of similarity to their ancestors.
One way to look at this is in Richard Dawkin’s “The Ancestor’s Tale” which ends with eubacteria as our most distant relative.
You better believe they have. And most likely they’ve been doing it faster than we have, given the generation time. It may not look impressive to our eyes, but microorganisms are exquisitely evolved to their environments. There’s more to life than multicellularity.
If I were to use a sig, I’d want this. Actually, I’d like this as a tee shirt, maybe with a diatom on it.
Here you go the entire tree of life.
http://www.zo.utexas.edu/faculty/antisense/DownloadfilesToL.html
Depending on definition, flowering plants may be the correct answer, though for a somewhat different reason than Quartz gives.
If humans and chimps each have, say, 50000 genes of which 48000 are the same (I made these numbers up), then the difference is 4000 genes: the 2000 humans have that chimps don’t and the 2000 genes vice versa. By this definition, humans would be only “49900 genes different” from a very primitive creature, but “100,000 genes different” from an equally complex creature sharing no genes.
As seen in a page with a graph showing amount of genetic material, flowering plants may have the most genetic material of any creature and it is mostly different (I’m guessing) from humans’.
Actually, there’s a surprising amount of genetic material in common between all life on earth. Between humans and chimps, for example, something like 98% of our genes are identical. Between humans and plants, if I recall correctly (and I could be off on this) there might be as much as 60% of genes held in common, so that’s not “mostly different”.
My vote would be for something among the Archaea extremophiles.