Though the Department of State has been keeping copies of correspondence since its earliest days, recordkeeping was decentralized until 1870. The records for 1789-1906 are now arranged in three series: Diplomatic Correspondence; Consular Correspondence; and Miscellaneous Correpondence, and the period from 1906-1910 is covered by the "Numerical Files."
The bulk of the records for 1789-1910 were microfilmed between 1941 and 1982, and the material is widely available at libraries. Princeton holds many of the microfilm publications covering this period, and others are available to Princeton researchers through Interlibrary Loan. Diplomatic Records: a select catalog of National Archives microfilm publications, a sales catalog published in 1986, is still an excellent guide to what is available, and is indexed by country. There is a copy in the history librarian's office. The researcher can also consult NARA's online microfilm catalog: http://www.archives.gov/publications/microfilm-catalogs.html. See http://www.archives.gov/publications/microfilm-catalogs.html#diplomatic for advice on how to limit your search to diplomatic records.
A new filing system was used between 1906 and 1910; it was eventually found unsatisfactory and was replaced by the Decimal File system. The records from the Numerical File have been microfilmed, and the set includes 1,241 reels. CRL holds part of this set, Numerical and minor files of the Department of State, 1906-1910 [microform].
The main series are "Despatches from U.S. consuls in [city] [country], [date]" and "Despatches from U.S. ministers to [country] [date]"
They were microfilmed by the National Archives and distributed by Scholarly Resources, now a part of Gale CENGAGE. There is a list in Diplomatic Records: a select catalog of National Archives microfilm publications.
We have many of the consular series, but only a few from the ministerial series. Search the library catalog for keywords "despatches consuls [country]" to find out what we have.
In addition to the consular & diplomatic correspondence, there are several other series covering correspondence with foreign legations and consulates. Princeton holds very little of this material, but more is available from CRL. Search the CRL catalog for "foreign legation department state" for a list.