Conversely, when a stretch of DNA is observed to code for an important function in the organism, it is a pretty solid guess that it is highly conserved by purifying selection. Survival and/or reproduction is difficult* without the function, so any changes to that DNA is not tolerated by natural selection.
There are many examples of this, so there is not a lot of contention over this issue. I mean, there isn't any, at all.
But now two guys at Stanford University has come along and destroyed this pretty picture. McLean and Bejerano have in mice discovered ultraconserved non-exonic elements (stretches of DNA that do not code for a protein), which do not cause a phenotype when deleted (source). In other words, while this DNA is highly conserved, showing strong purifying selection during the evolutionary history of mice, the mice seem to do fine without it. It doesn't seem to serve any function that the mouse can't do without. Astonishing!
What is going on? Surely this DNA must be doing something? McLean and Bejerano will now make a thorough investigation into the matter, and hopefully unravel this mystery.
One suggestion is that the ultraconserved DNA plays a role under some circumstance that the mice are not subject to in the laboratory. After all, the sheltered life of a lab mouse is quite different from that of wild mice. Any number of environmental conditions that are in effect outside the lab and not inside could explain the necessity. Pathogens, perhaps? It turns on expression of genes that produce a venom when the mice are eaten, maybe? Could it be that it is involved in some higher cognitive function that only Douglas Adams knew about?
McLean, Bejerano (2008). Dispensability of mammalian DNA Genome Research
* I know, I know. This is Mission Impossible. Difficult should be a walk in the park.