You should read this paper if you want a nice summary of the evidence for a high percentage of junk in our genome. They cover genetic load, sequence conservation, and the evidence from the genome sequence itself. There's a brief description of the nearly-neutral theory of molecular evolution and why it's relevant to the debate.1
One of the most important contributions is an explanation of the C-Value Paradox and the Onion Test. The Onion Test was originally published on Ryan's blog (The onion test) but some people won't reference blog posts so here it is in a peer-reviewed paper.
There are several key points to be understood regarding genome size diversity among eukaryotes and its relationship to the concept of junk DNA. First, genome size varies enormously among species , : at least 7,000-fold among animals and 350-fold even within vertebrates. Second, genome size varies independently of intuitive notions of organism complexity or presumed number of protein-coding genes (Figure 1). For example, a human genome contains eight times more DNA than that of a pufferfish but is 40 times smaller than that of a lungfish. Third, organisms that have very large genomes are not few in number or outliers—for example, of the >200 salamander genomes analyzed thus far, all are between four and 35 times larger than the human genome . Fourth, even closely related species with very similar biological properties and the same ploidy level can differ significantly in genome size.
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 .
1. A little birdy tells me that there's a "better" paper coming out in a few months.
Palazzo, A. and Gregory T.R. (2014) The Case for Junk DNA. PLoS Genetics (published May 8, 2014) [doi: 10.1371/journal.pgen.1004351]