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Bibliographies are, in fact, implemented as lists, so all the confusion about reducing list item spacing also applies to bibliographies.

If the natbib package ‘works’ for you (it may not if you are using some special-purpose bibliography style), the solution is relatively simple — add

\usepackage{natbib}
\setlength{\bibsep}{0.0pt}

to the preamble of your document.

The compactbib package has a similar effect. Its primary purpose is to produce two bibliographies, and it seems to preclude use of BibTeX (though the package documentation, in the package file itself, isn’t particularly clear).

Otherwise, one is into unseemly hacking of something or other. The mdwlist package actually does the job, but it doesn’t work here, because it makes a different-named list, while the name “thebibliography” is built into LaTeX and BibTeX. Therefore, we need to patch the underlying macro:

\let\oldbibliography\thebibliography
\renewcommand{\thebibliography}[1]{%
  \oldbibliography{#1}%
  \setlength{\itemsep}{0pt}%
}

The savetrees package performs such a patch, among a plethora of space-saving measures: you can, in principle, suppress all its other actions, and have it provide you a compressed bibliography only.