How to order citations by appearance using BibTeX?

Question

By default (using the plain style) BibTeX orders citations alphabetically.

How to order the citations by order of appearance in the document?

Answer 1

The best I came up with is using the unsrt style, which seems to be a tweaked plain style. i.e.

\bibliographystyle{unsrt}
\bibliography{bibliography}

However what if my style is not the default?