Horizontal gene transfer

Horizontal Gene Transfer is a rather… unusual phenomenon in biology. Under normal circumstances, a population will acquire new genes through mutations, and if the genes are beneficial they reproduce, but if not they won't. Horizontal gene transfer is where organisms acquire genes via means other than the typical parent-offspring route, and can occur within or between species.

Bacterial transformation
As the name implies, this occurs in bacteria. A bacterium may consume DNA from its surroundings, and incorporate said DNA into its own. This can be an advantage since bacteria are most likely to acquire the DNA from the organisms that are most common in an environment, which are probably the ones that produce chemicals including proteins that help them even exist in said environment. It's especially useful for organisms that reproduce asexually, who can't pair their DNA with other 'successful' partners. The result is that organisms like Escherichia coli that exist in your intestines can acquire anti-biotic resistance from other strains of bacteria.

Bacteria also acquire genes through bacterial conjugation. Yes, bacteria "mate", and this enables useful genes to hop between different strains of bacteria.

Virus mediated transfers
A virus is a chunk of RNA or DNA surrounded by a delicious candy coating protein shell that injects itself into another cell, fusing its genetic material with the cell's DNA. The result is a 'reprogrammed' cell, and usually the cell will then cease most other functions and begin mass producing more viruses, bursting open to flood you with more viruses to infect more cells and repeat the process. In other words, a viral infection is where part of you becomes the virus. Not all viruses instantly turn your cells into virus factories; HIV, infamously, will turn a number of cells into a "reservoir" that produce viruses at a later date, months years or even decades after initial infection, making a cure for AIDS virtually impossible (though a vaccine or other possible treatments are theoretically possible).

In very rare cases, when adding to the DNA code the virus ends up creating a cell that does not ever turn into a "virus factory". The result is a cell with DNA different than surrounding cells. A virus could be loaded with things like fungi DNA, and add to a cell in a beetle, for example. If the altered cell happens to be a gamete (sperm or egg), the organism will contain genes that did not originate from either of its parents. Much like regular mutations, this is often detrimental or fatal to the organism, but not always.

Artificial horizontal gene transfer (aka GMO)
Humans can attempt to induce a specific gene transfer from one organism to another via a number of methods. The goal of this, aside from being awesome, is to produce food that grows more efficiently, doesn't rot as quickly, is resistant to pests, or just. This is nothing that doesn't already happen in the wild; it's just faster and unlike the wild, regulated. So, ironically, safer than nature.

"Disproving" evolution/Inevitable creationist drivel
The original model of evolution has undergone quite a bit of adaption since Darwin/Wallace first wrote it down. While the theory in its original form predicted some form of 'record keeping' that would enable offspring to inherit parents' attributes, Darwin did not know how this 'record' was stored and what altered it. Darwin also did not know how inheritance worked like exactly, even though Gregor Mendel (the guy who actually discovered this) was alive around this time. Sadly, Mendel did not publish any of his findings in any widely read journal or indeed in English. Even more sadly, Darwin was one of the few people who did have access to Mendel's work... but stopped reading before he got to the important parts. Originally Darwin conjectured that the record was stored in the blood; this was proven false by blood transfusion animal experiments conducted by Darwin's cousin Francis Galton. Galton would spend quite some time trying to determine the nature of the record, even performing experiments on snow peas, the same species that Mendel discovered Mendelian Genetics from. But Galton was too clever by half; his records were continuous while it turns out genetics is discrete. Darwin also conjectured Sexual selection as well as Natural selection, but Victorian sensibilities prevented people from accepting the idea that the female ever had any say in choosing who mates with her.

Even with the theory evolving since Darwin's day, and the discovery of DNA, DNA was thought to only be altered via mutation. And addition, deletion, duplication, inversion, shuffling, regular old errors, and OK there a lot of things that can happen. But not taken from completely foreign DNA.

Since something not predicted by the original models of evolution has been discovered, it obviously means that all of evolution is wrong and since there are only two possibilities for life on Earth, Creationism is right, right? Obviously not, but that doesn't prevent some people from quote-mining actual scientists. Nor does it help that the scientist spearheading the research into HGT, Dr. Doolittle, is a tad arrogant and thinks he knows more than the scientists who work on other projects.

Examples in the natural world

 * Sometime during the Cretaceous Period, exploded in biological diversity. They did so at a time when  (or "flowering plants") were becoming more common and causing older families to become rarer, like    (probably), and to a much lesser extant  Paleontologists were perplexed as to why ferns, which were practically living fossils by the Cretaceous, should undergo such a monumental surge in biological diversity at a time when the diversity of many major non-angiosperm clades was declining.  At some point during the Cretaceous a fern somehow ended up with a gene called neochrome that helped it survive in dim light, it prospered and its descendants prospered. The fern in question did not evolve its neochrome gene; it stole it.
 * Aphids and red spider mites are the only two animal species/genera that can create red carotenoids. The damned bugs apparently acquired these genes from a fungus proving once and for all transferring genes can only lead to superbugs .  Damn aphids.
 * Homo sapiens, aka humans, have 145 genes that likely came from other species. That's right, you are a freak created by SCIENCE! (cue dramatic music, lightning).  Or really, nature just doesn't give a damn about your quaint ideas of "decency", and the definition of "human" isn't nearly as clear-cut as we like to pretend.