A digital object identifier (DOI) is a globally unique string that identifies an electronic document (for example, a PDF of an academic article). It essentially provides a method for creating a permalink to a document (for example, http://dx.doi.org/10.1145/146585.146609).
Is there a web service (or any other system) to get the metadata (preferably in BibTeX form) of a document from a given DOI?
Edited to add some expository information.
Answer
Section 5.4.1 Content Negotiation of the DOI Handbook documents states, "Content negotiation is being implemented by DOI Registration Agencies for their DOI names, specifically to offer value-added metadata representations for users." According to Section 4 Supported Content Types of the DOI Content Negotiation documentation for http://crosscite.org, "Currently three DOI registration agencies have implemented content negotation for their DOIs: CrossRef, DataCite and mEDRA." The list of supported formats (which depends on the registration agency) includes both BibTeX via Accept: application/x-bibtex (this is the approach used by http://doi2bib.org) and formatted bibliography entry via Accept: text/bibliography (this is the approach suggested by @anumi above). When using the latter header, you must specify the style=bibtex media type parameter.
The two relevant mimetypes provide slightly different representations. A request to GET http://dx.doi.org/10.1038/nrd842 with Accept: application/x-bibtex yields the response
@article{Atkins_2002,
doi = {10.1038/nrd842},
url = {http://dx.doi.org/10.1038/nrd842},
year = 2002,
month = {jul},
publisher = {Springer Nature},
volume = {1},
number = {7},
pages = {491--492},
author = {Joshua H. Atkins and Leland J. Gershell},
title = {From the analyst{\textquotesingle}s couch: Selective anticancer drugs},
journal = {Nature Reviews Drug Discovery}
}
and with Accept: text/bibliography; style=bibtex
@article{Atkins_2002, title={From the analyst’s couch: Selective anticancer drugs}, volume={1}, ISSN={1474-1784}, url={http://dx.doi.org/10.1038/nrd842}, DOI={10.1038/nrd842}, number={7}, journal={Nature Reviews Drug Discovery}, publisher={Springer Nature}, author={Atkins, Joshua H. and Gershell, Leland J.}, year={2002}, month={Jul}, pages={491–492}}