Darwin said that humans and monkeys have a common ancestor (around 5-10 million years ago), freaking out creationists by the fact that humans are apes. Therefore, humans sit on the same branch of the evolutionary tree as great ape species, such as chimpanzees, our closest living primate relative.
By comparing human and chimpanzee genomes, a long-awaited milestone, scientists stimated that the number of base pairs we share with them are around 95-98%. In addition, the small percentage that is different is not very interesting, involving features such as immune responses and sperm surface proteins.
What makes chimpanzees and humans different?
Although we share most of the genome, humans and other big apes, such as chimpanzees are very different.
How did we become human? The answer lies not in the similarities of our genes as such, it is in how our genes interact and work, the presence of small mutations and differences in gene expression mainly mediated by regulatory molecules.
Therefore, despite big similarities, minor differences between humans and chimpanzees could turn out to be critical.
Cohen, J. Evolutionary biology. Relative differences: the myth of 1%. Science (2007)
Varki, A. et al. Comparing the human and chimpanzee genomes: Searching for needles in a haystack. Genome Research (2005)