LaTeX stopped building a BibTeX bibliography, how to troubleshoot it?

Summarised (and expanded) from comments above:

BibTeX uses the aux file written by LaTeX (showing where you want to cite what) together with a bst file (containing stylistic information - such as plain.bst) and a bib file (containing bibliographic information about any document you might want to reference). So a workflow from the command line might look like

1. latex - to generate the aux file
2. bibtex - to generate a bbl file which contains information about the specific references mentioned in the aux file, formatted correctly
3. latex - to incorporate the information in the bbl file into your typeset document
4. possibly latex again, to fix any cross-referencing problems introduced when all the citations were included

Looking at the aux and bbl files along the way - and, as @Joseph pointed out, the blg file which is BibTeX's log - can help to troubleshoot problems.

For completeness as an answer: on this occasion it apparently turned out that the bibtex step wasn't working due to a typo in the name of the bst file.