Many institutions have Linnaean material available online. Here are some useful links:
Carl Linnaeus's printed books
The Linnean Society of London has digitised 197 titles from Linnaeus's personal library, through the generous support of the Andrew W. Mellon Foundation, which are freely available online. They include books that Linnaeus used as reference material; all theses of his students that he supervised; and Linnaeus' personal copies of his own works, spanning from 1735 to 1776, many of them interleaved and copiously annotated in his own hand.
The Hunt Institute also provides access to two Linnaeus-related databases: "Index to Binomials Cited in the First Edition of Linnaeus' Species Plantarum" and "Index to Scientific Names of Organisms Cited in the Linnaean Dissertations".
Uppsala University Library has the Hammarby Collection, consisting of works that belonged to Linnaeus's own library. These books, mainly about medicine, were part of the collections that were sold by Linnaeus's widow to The Linnean Society of London, but they were later returned to Sweden at the end of the 19th century on the grounds that they did not fit in subject-wise.
Digitised Linnaean titles can also be found in the Staatsbibliothek's database of 18th-century printed books of German-speaking countries, VD18.
Carl Linnaeus's correspondence
The Linnaean Correspondence Project publishes the complete text of the letters sent and received by Carl Linnaeus, together with summaries in English. Facsimiles of the original manuscripts and of selected printed editions are provided.The texts, summaries and facsimiles are linked to a master database of the correspondence and to files providing biographical and bibliographical information on the correspondents and their works. The texts and the summaries are searchable, as is the database.
The Linnean Society of London's Linnaean Correspondence Collection can also be searched online.
Carl Linnaeus's manuscripts
The Linnean Society has catalogued and digitised its Linnaean Manuscripts Collection, which is closely related to the Linnaean Collection of botanical and zoological specimens. The manuscripts are the basis for Linnaeus's published works and the foundation of modern taxonomy. They can be searched by author, title, or date.
Carl Linnaeus's specimens
The Swedish Museum of Natural History holds Linnaean specimens, including herbarium sheets, as well as zoological specimens.