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It is possible to write your own: the standard bibliography styles are distributed in a form with many comments, and there is a description of the language in the BibTeX distribution (see BibTeX documentation). However, it must be admitted that the language in which BibTeX styles are written is pretty obscure, and one would not recommend anyone who’s not a confident programmer to write their own, though minor changes to an existing style may be within the grasp of many.

If your style isn’t too ‘far out’, you can probably generate it by using the facilities of the custom-bib bundle. This contains a file makebst.tex, which runs you through a text menu to produce a file of instructions, with which you can generate your own .bst file. This technique doesn’t offer entirely new styles of document, but the system’s “master BibTeX styles” already offer significantly more than the BibTeX standard set.

An alternative, which is increassingly often recommended, to use biblatex. Biblatex offers many hooks for adjusting the format of the output of your ‘basic’ BibTeX style, and a collection of ‘contributed’ styles have also started to appear.