In Nature Lamprecht et al provide evidence that the presence of long terminal repeats (LTRs, a form of junk DNA) increases the risk of humans' developing certain cancers, especially lymphomas. [Added later: in 2007 the ENCODE study was supposed to show evidence that intragenic regions are pervasively transcribed but there's a large segment that believes this to be an artifact.]
Initially the discovery that our genomes were to a first approximation entirely composed of non-coding garbage characters was a surprise. But on further evolutionary reflection, it made sense: DNA is about copying itself, and it sometimes codes for proteins in networks with other pieces of DNA as a replication strategy. Consequently we should expect that most DNA is passively or selfishly just along for the ride, except in highly fecundity-dependent species where the extra time and energy make a fitness difference (like bacteria). Before you make the effort to back-of-the-envelope calculate the daily cost of replicating the 97% extra noncoding portion of our genome, realize that I have doubtless expended more calories typing this blog post than I will expend from all the DNA replication and proofreading I do during the entire day.
But even if the energy expended is not a problem, this paper revives the debate, because it shows that there still is a fitness cost for junk DNA in multicellular organisms - but it's paid in terms of cancer risk rather than energy cost. It's a little harder to write this off as fitness noise. We're back to the old question of what the advantage is for multicellular organisms to carry so much junk DNA.