This list is offered as an aid to further reading and research. For more detailed and precise bibliographic information, collector-oriented, ABAA has the indispensable article
A Checklist of Herman Melville's First and Major Editions by Kevin MacDonnell.
What I have so far, chronologically from Typee to Timoleon (electronic text only):
Narrative of a Four Months' Residence Among the Natives of a Valley of the Marquesas Islands. London, 1846. First British edition of Typee, published in London by John Murray. Digitized volume in the Wellcome Library; available online courtesy of the Internet Archive.
Typee, 1846 --Wiley and Putnam NY edition, two parts in one volume, with Story of Toby. University of California Libraries book at archive.org
Typee, 1847 --London edition, University of Michigan copy in the Hathi Trust Digital Library.
Typee, 1847 --Revised edition, NY Wiley & Putnam in one volume with Story of Toby and excerpted reviews in publisher's advertisements. Harvard copy at Hathi Trust.
Typee, 1847 revised American ed. in one volume. Michigan copy at Google Books.
Typee, 1847 revised American edition. Same as above, in the Hathi Trust Digital Library.
Typee, 1892 --with Melville's portrait as frontispiece.
Omoo, 1847 --NY Harper & Brothers edition, University of California Libraries copy at archive.org
Mardi; and a Voyage Thither, vol 1 --1849, first American edition. University of California Davis copy at HathiTrust.org
Mardi Volume 1 at Google Books
Mardi: and a Voyage Thither Volume 1 - 1849 first edition; University of of Pittsburgh copy via Internet Archive.
Mardi; and a Voyage Thither, vol 2 --1849, first American edition. University of California Davis copy at HathiTrust.org
Mardi Volume 2 (1855 ed.) at Google Books
Mardi: and a Voyage Thither Volume 2 - 1849 first edition; University of of Pittsburgh copy via Internet Archive.
Redburn: his first voyage --1850, NY Harper & Brothers. University of Michigan copy at HathiTrust.org
White-Jacket, vol 1 --1850 London edition, Richard Bentley. Bodleian Library copy at archive.org
White-Jacket, vol 1 --same as above, 1850 London edition at Google Books. Where is volume 2?
White-Jacket, 1892--later printing of the 1892 edition by St Botolph Society in cool blue binding, University of Wisconsin Library book at HathiTrust.org
Moby-Dick, or, the Whale --1851, First American Edition. Duke University, Rubenstein Library copy (with clipped signature of Melville pasted in) at HathiTrust.org
Moby-Dick, or, the Whale --same as above, online at archive.org
1952 Hendricks House Moby-Dick --Important edition with great explanatory notes by Luther Mansfield and Howard Vincent.
Pierre, or, The Ambiguities --1852 first edition, Harvard copy at HathiTrust.org
Pierre, 1852 --same as above, online also at archive.org
Israel Potter: his fifty years of exile --1855 book version, first edition thus. Bodleian Library volume at archive.org
The Piazza Tales --1856 first edition, Stanford University Library volume at Google Books
The Confidence-Man: his masquerade --1857 first American edition with bookplate of B. George Ulizio, also with stamp of Powers Library, Moravia, NY at archive.org
The Confidence-Man: His Masquerade; Via Google Books, the Bodleian copy of the "Authorised Edition" published in London by Longman's.
1954 Hendricks House Confidence-Man , edited by Elizabeth S. Foster
Battle-Pieces --1866 first edition at Google Books
Battle-Pieces and aspects of war --another 1866 edition, University of California volume at archive.org
Clarel, A Poem and Pilgrimage in the Holy Land --Volume 2 of the 1876 first edition (New York: G. P. Putnam's Sons) at Ohio Sate University via Hathi Trust Digital Library. Where's volume 1?
Clarel, Hendricks House 1960 --the great groundbreaking edition by Walter E. Bezanson
Wikisource gives the text of Clarel from the Hendricks House editionJohn Marr and Other Sailors --online electronic text of the first edition (1888) by Paul Royster, University of Nebraska-Lincoln
Timoleon, Etc. --online electronic text of the first edition (1891) by Paul Royster, University of Nebraska-Lincoln
The Works of Herman Melville volume 16 - Poems. Constable edition, 1924 courtesy of Hathi Trust Digital Library.
Posthumously Published WorksBilly Budd --Versions of Billy Budd via Melville Electronic Library
Houghton Library, Harvard University has the Billy Budd manuscriptBilly Budd, Sailor and Other Uncompleted Writings - Northwestern-Newberry Edition with Weeds and Wildings, Parthenope (includes "At the Hostelry" and "An Afternoon in Naples in the Time of Bomba"); Uncollected Prose and Uncollected Poetry.