@Perplexed (quoting blossomberrry)
It is selection pressure. This has been confirmed in the lab via direct observation and experimentation.

A great example to show this is the evolution of nylonase in flavobacteria. Nylon is a completely synthetic product which did not exist in the environment until it was first created in 1935. In 1975, researcher discovered that one strain of flavobacterium was able to metabolise this completely synthetic product. Further investigations found that a gene duplication and frame shift mutation had occurred to one of it's genes which resulted in a completely new enzyme, now named nylonase. As a further test to the power of evolution via natural selection, another group of scientists grew a culture of Pseudomonas bacteria in an environment high in nylon. These bacteria were unable to metabolise nylon at the beginning of the experiment. Nothing occurred for many generations and then a completely different mutation occurred which resulted in a new and different nylonase enzyme.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC345072/
http://en.wikipedia.org/wiki/Nylon-eating_bacteria

Another fantastic example is the Lenski experiment (LTEE) using the bacteria E.coli. One of the key attributes of E.coli is it's inability to transfer citrate across the cell membrane. 12 samples of this bacteria have been cultured over 20 years in isolation to see how evolution and selection acts on these independent cultures. Lenskis team would take a sample of each culture and freeze them every 500 generations so as to be able to look back in time at any of the 12 cultures to see any key mutational changes to their genome. A mutation occurred somewhere between generations 31,000 and 31,500 in one of the populations which resulted in the ability for the organism to transfer citrate across the cell membrane and therefore include this in it's citric acid cycle. This is another great example of evolution by natural selection adding new information to a genome and therefore a brand new biochemical pathway which provide an advantage to the organism.

http://aem.asm.org/cgi/reprint/61/5/2020.pdf
http://en.wikipedia.org/wiki/E._coli...ion_experiment

@Perplexed
Unless vestigial structures are exapted for another purpose they are eventually dropped. The question is timeline. We are in the process of dropping them if they are functionless. If however, the structures are exapted for something other than their original function, they may remain in a vestigial state. Whilst the appendix is a vestigial form of the cecum, it may now still provide some beneficial function to assist in the culturing of symbiotic bacteria which aids digestion. The coccyx is the remnant of a tail (which is still present during stages 14 to 22 of human embryogenesis). Whilst the primary function of assisting mobility, balance or even a prehensile function no longer exists, it still possesses secondary functionality of muscle attachment which may limit (provide selection pressure) for retaining it.