Jonathan Schooler argues in favour of an open-access database of negative results (Nature 470, 437; 2011). But publishing such results in scientific journals is advantageous for authors, who can then list them among their papers.
Several journals specifically publish negative results. I'm aware of the Journal of Negative Results in Biomedicine, the Journal of Negative Results — Ecology and Evolutionary Biology and the psychology Journal of Articles in Support of the Null Hypothesis. There is a forum in the Journal of Universal Computer Sciences for negative results, and PLoS ONE also publishes them. Several other such journals have come and gone; all, I think, are open access.
Even so, negative findings are still a low priority for publication, so we need to find ways to make publishing them more attractive.