Our closest relative is the bonobo followed by very little difference by the chimpanzee we share a amazing 98.9% and 98.5% respectively of our DNA with them!! and they share around the same percentage between themselves, however we have 1.6% of our DNA that we share with Bonobos but not with Chimpanzee and the same amount we share with Chimpanzee and not Bonobos, what suggests that the 3 species separated a while back around 4 million years ago.
Scientist are not entirely sure what the differences in DNA in the three species today is, but they seems to think they are related to perception of social clues, regulate immune responses and tumor suppression genes.
We also share about 50% of our DNA with a banana and also have many genes that structurally are similar to those from Sponges too! By this I mean the following: The major hypothesis that underlies Darwin’s theories of evolution is the tree of life. Taken to its logical conclusion it means that eukaryotic life can should be able to be traced back to the Last Common ancestor which is why the search has included understanding and looking at even single celled organisms called Achaea found most often in hot thermal vents at the bottom of the Ocean. From that life emerged in a multi-cellular form first most likely something similar to the Choanoflagellates we find today (see https://en.wikipedia.org/wiki/Choanoflagellate ). Next step took place during the Cambrian explosion over 550 million years ago when life forms of amazing diversity arose that eventually became the Metazoan lineage (animals) with a body plan that is still retained to this day! Sponges were an early off-shoot that came sooner then this stage as the fossil records tell us but survive to this day due to their lifestyle and wide niche in which they are found.
To make the goose centric answer (seeing as damselfly has already given you the correct answer). Humans share a lot of DNA with birds (~65%) depite diverging over 300 million years ago.
The amount of shared DNA may surprise you, but consider that humans have some of the same proteins that bananas have. It may also be that genes that are shared by banana, human and fruit fly may have what look like different functions.
For example, a gene in the worm C. elegans involved in development of the heart is similar to a gene in fruit flies that makes female fruit flies receptive to males for mating. A version of this gene in humans is important in hearing. All because the protein that the gene makes performs a function that is important in lots of processes in different animals.