One would expect you to do a simple Google search. This comes up - http://message.snopes.com/showthread.php?t=51513
Any reference to a "percent similarity" between two species has all kinds of problems.
Like Nick said, if you just pick a random place on both genomes and start comparing "sequences" you'll get about a 25% match.
But DNA "sequence" is much more than just the pattern of A,T,G and C. The chromosomal location, nearby genes, methylation, amount of "junk" DNA in the vicinity and a bunch of other things contributes to what a particular sequence actually does (which is a much more relevant thing to compare than just raw sequence).
The genomes of most higher species is roughly 90% "junk". That "junk" is very poorly conserved across species. "Non-junk" DNA, that actually codes for a protein or acts as a regulatory element, is much more highly conserved across species but at only ~10% of the genome it really doesn't contribute all that much to the overall similarity.
You often see quotes saying how similar the DNA is between two species. In most situations the number is meaningless since how similar the genomes are depends on how you define similarity. There are a couple ways to define similarity and each method is used to examine different aspects of the DNA sequences. Quotes like "a chimp's DNA is 95% identical to humans" is very misleading. That particular comparison was almost certainly done on just the coding sequences, which is only ~10% of the genome. The noncoding DNA is much less conserved across species, and even between individuals of the same species.
If you abstract the comparison one more level, to protein sequence, the similarities between species increases. Indeed I suspect most comparisons you see between humans and other primates is actually at the protein level.
But back at the genome wide level the similarities aren't all that great and measuring the similarity at that level really doesn't have all that much value.
Another thing to consider when comparing genomes is that nobody really knows the relationship between the number of genes and the "complexity" of the organism. Or, how a small change in a single gene can significantly change the gene's behavior, and potentially the complexity of the organism. The simple minded thought that "complexity" is a linear function of the number of genes is certainly wrong. Even though scientists that should know better often treat gene number as being a linear measure of complexity. When the human genome was nearing initial completion there were a fair number of scientists that thought there was something seriously wrong with the methods used because the number of genes was turning out to only be ~30,000. That isn't all that many, something like 6x more than bacteria. "Certainly humans are more than 6x more complex than bacteria" was a fairly common thought but it is erroneous because gene number is not a valid measure of the organism's complexity.
The fact is "complexity" isn't linear in the number of genes and isn't even constant for a fixed number of genes. So even if humans and bananas share 50% of their sequences that does not really say anything about the actual relatedness, or the relative complexity, of the two species.
"Relatedness" can be determined by comparing the genomes of two species but that is a much more complex analysis than simply "we share 50% of our DNA with bananas." Any quote like "we share XX% of our DNA with {insert species name}" really has no significance, especially if you don't know what was actually being compared.
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****So it is not the number of chromosomes or nucleotides or proteins that determine the complex of an organism. It is something else.****
****But even more interesting is that the same stuff is used over and over again, in all kinds of organisms. With random this's and that's, one would expect more diversity. Not so!"***