Palazzo and Gregory cover the main lines of evidence which argue against the belief that most, if not all, of the genome is functional:
Pseudogenes: "...although some pseudogenes have been co-opted for organism-level function...most are simply evolving without selective constraints on their sequences and likely have no function."
Transposable elements: "Because of their capacity to increase in copy number, transposable elements have long been described as “parasitic” or “selfish”. However, the vast majority of these elements are inactive in humans, due to a very large fraction being highly degraded by mutation. Due to this degeneracy, estimates of the proportion of the human genome occupied by TEs has varied widely, between one-half and two-thirds...Many examples have been found in which TEs have taken on regulatory or other functional roles in the genome. In recognition of the more complex interactions between transposable elements and their hosts, Kidwell and Lisch proposed an expansion of the “parasitism” framework where each TE can be classified along a spectrum from parasitism to mutualism. Nevertheless, there is evidence of organism-level function for only a tiny minority of TE sequences. It is therefore not obvious that functional explanations can be extrapolated from a small number of specific examples to all TEs within the genome."
Highly Repetitive DNA: "Another large fraction of the genome consists of highly repetitive DNA...Many repeats are thought to be derived from truncated TEs, but others consist of tandem arrays of di- and trinucleotides. As with TEs, some highly repetitive sequences play a role in gene regulation...Others, such as telomeric- and centromeric-associated repeats, play critical roles in chromosomal maintenance. Despite this, there is currently no evidence that the majority of highly repetitive elements are functional."
Introns: "Although introns can increase the diversity of protein products by modulating alternative splicing, it is also clear that the vast majority of intronic sequence evolves in an unconstrained way, accumulating mutations at about the same rate as neutral regions. Although the median intron size in humans is ~1.5 kb, data suggest that most of the constrained sequence is confined to the first and last 150 nucleotides." [1]
As powerful as these argument are, perhaps the most compelling line of evidence is the lack of clear correlation between genome size and organism complexity. The graph below makes this point clear:
These observations pose an important challenge to any claim that most eukaryotic DNA is functional at the organism level. This logic is perhaps best illustrated by invoking “the onion test”. The domestic onion, Allium cepa, is a diploid plant (2n = 16) with a haploid genome size of roughly 16 billion base pairs (16 Gbp), or about five times larger than humans. Although any number of species with large genomes could be chosen for such a comparison, the onion test simply asks: if most eukaryotic DNA is functional at the organism level, be it for gene regulation, protection against mutations, maintenance of chromosome structure, or any other such role, then why does an onion require five times more of it than a human? Importantly, the comparison is not restricted to onions versus humans. It could as easily be between pufferfish and lungfish, which differ by ~350-fold, or members of the genus Allium, which have more than a 4-fold range in genome size that is not the result of polyploidy.
In summary, the notion that the majority of eukaryotic noncoding DNA is functional is very difficult to reconcile with the massive diversity in genome size observed among species, including among some closely related taxa. The onion test is merely a restatement of this issue, which has been well known to genome biologists for many decades. [2]
Any argument about intelligent design versus evolution comes to a screeching halt when the genomic evidence is examined. To paraphrase Dobzhansky, nothing in genomics makes sense except in the light of evolution.
References
1. Palazzo AF, Gregory TR (2014) The Case for Junk DNA. PLoS Genet 10(5): e1004351. doi:10.1371/journal.pgen.1004351
2. ibid